document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161304>Question 1161304</A>: <I><SPAN STYLE=\"word-break: break-all;\">  x2  -  x  -  1 = 0 Let x = j\r<BR>\n" );
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document.write( "j2  -  j  -  1= 0 Isolate j2\r<BR>\n" );
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document.write( "j2 = 1 + j Take the square root of both sides\r<BR>\n" );
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document.write( "j= √1 + j Now we know that the value of j is 1 + j\r<BR>\n" );
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document.write( "j= √1 + √1+⋯\r<BR>\n" );
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document.write( "Iteration #1: j= √1 + √1\r<BR>\n" );
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document.write( "Iteration #2: j= √1 + √1+√1\r<BR>\n" );
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document.write( "Show how we can use iterations of this nested radical to find the value of j. How many iterations do we need to do to get close to the value we calculated in 1)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784815 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=784815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "No.  Your entire premise is faulty.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ x\ -\ 1\ =\ 0\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ j\">\r<BR>\n" );
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document.write( "Ok, but the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j\"> substitution has no value that I can see.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ j^2\  -\  j\  -\  1\ =\ 0\">\r<BR>\n" );
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document.write( "Isolate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large j^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ j^2\ =\ 1\ +\ j\">  That's ok\r<BR>\n" );
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document.write( "Take the square root of both sides\r<BR>\n" );
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document.write( "Here is where you go high and right:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ j\ \neq\ \sqrt{1}\ +\ j\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ j\ =\ \pm\sqrt{1\ +\ j}\ \neq\ 1\ +\ j\">\r<BR>\n" );
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document.write( "The idea that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE j\ =\ 1\ +\ j\"> is ludicrous.  If that were true, you could subtract j from both sides and get 0 = 1.\r<BR>\n" );
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document.write( "The rest of your post is nonsense.\r<BR>\n" );
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document.write( "I think what you were trying to get to was:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{1\,+\,\sqrt{1\,+\,\sqrt{1\,+\,\sqrt{1\,+\,\sqrt{1\,+\,...}}}}}\">\r<BR>\n" );
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document.write( "In which case you need at least 10 iterations to be correct to the 4th decimal place. This method converges very slowly.\r<BR>\n" );
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document.write( "The 19th Fibonacci number divided by the 18th Fibonacci number gets you 5 decimal place accuracy with a crapload less arithmetic.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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