<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">a</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="real_1.html#NM1">Real</a>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp;  <a href="polyeq_1.html#K8">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:12"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i>, <a class="ref" href="polyeq_1.html#D4">POLYEQ_1:def 4</a></i>;<br/>
<a NAME="E3:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E4:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E5:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E6:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E7:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E8:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="power.html#K4">to_power</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="power.html#T31">POWER:31</a></i>;<br/>
<a NAME="E9:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K3">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default">1 <a href="newton.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="power.html#T48">POWER:48</a></i>;<br/>
<a NAME="E10:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default">1 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E11:12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> 1</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E12:12"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:12_1_1"/>
( <font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R1">=</a> 0 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 )
 </span><b>by </b><i>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_1"><b>case </b></a><a NAME="E1:12_1_1_1"/>
<font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:12_1_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K6">-</a> 1
 ;<br/><b>hence </b><a NAME="E3:12_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="12_1_1_2"><b>case </b></a><a NAME="E1:12_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:12_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E3:12_1_1_2"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="polyeq_1.html#K3">Polynom</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">a</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="polyeq_1.html#D2">POLYEQ_1:def 2</a></i>;<br/><i><font color="Green">E24</font></i>:  <a href="quin_1.html#K1">delta</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>

;<br/><a NAME="E5:12_1_1_2"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> <font color="Maroon">a</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> <font color="Maroon">a</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="polyeq_1.html#T5">POLYEQ_1:5</a></i>;<br/><b>hence </b><a NAME="E6:12_1_1_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E14:12"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> )
 ;<br/>


</div>
