document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117379>Question 1117379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [sqrt(3+sqrt5)] - [sqrt(3-sqrt5)]^2 = 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #732462 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=732462\">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( "The statement given is not true because you are only squaring the 2nd term in the left-hand side.  If, as I suspect, you actually meant the problem to read:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \(\sqrt{3\ +\ \sqrt{5}}\ -\ \sqrt{3\ -\ \sqrt{5}}\)^2\ =^? \ 2\">\r<BR>\n" );
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document.write( "Then the proof is given below.\r<BR>\n" );
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document.write( "Expand the binomial in the LHS\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \(3\ +\ \sqrt{5}\)\ -\ 2\(\sqrt{3\ +\ \sqrt{5}}\)\(\sqrt{3\ -\ \sqrt{5}}\)\ +\ \(3\ -\ \sqrt{5}\)\ =^?\ 2\">\r<BR>\n" );
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document.write( "Collect like terms and calculate the product of conjugates in the center term of the LHS\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  6\ -\ 2\(\sqrt{9\ -\ 5}\)\ =^?\ 2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  6\ -\ 2\(\sqrt{4}\)\ \equiv\ 2\">\r<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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