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<b>let </b><font color="Maroon">p</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">q</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">y</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>assume </b><a NAME="E1:31"/><i><font color="Green">E34</font></i>: 
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> 1,0,<font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>let </b><font color="Maroon">u</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">v</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E2:31"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">v</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E3:31"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="newton.html#K2">|^</a> 3</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> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">v</font></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="newton.html#K2">|^</a> 3</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">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">u</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="newton.html#K2">|^</a> 3</span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">u</font> <a href="newton.html#K2">|^</a> 3</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">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">v</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="newton.html#K2">|^</a> 3</span>)</span>

;<br/>
<a NAME="E5:31"/><b>then </b><i><font color="Green">E38</font></i>: 
0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="newton.html#K2">|^</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">v</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">u</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">v</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">q</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:31"/>
3 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:31"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">v</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
 
;<br/>
<b>thus </b><a NAME="E8:31"/>
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">q</font>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E9:31"/>
<span class="p1">(<span class="default"><font color="Maroon">u</font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3
 <b>by </b><i>, <a class="ref" href="newton.html#T12">NEWTON:12</a></i>;<br/>


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