document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117328>Question 1117328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that [ sqrt(3 + sqrt(5)) - sqrt(3 - sqrt(5))]^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 #732370 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=732370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To ease the notation,  let  A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%283+%2B+sqrt%285%29%29+ ALIGN=MIDDLE  ALT=\"+sqrt%283+%2B+sqrt%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   and B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%283+-+sqrt%285%29%29+ ALIGN=MIDDLE  ALT=\"+sqrt%283+-+sqrt%285%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then the Left Hand Side is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28A+-+B%29+%5E2+ ALIGN=MIDDLE  ALT=\"+%28A+-+B%29+%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28A-B%29%5E2++=+A%5E2+-+2AB+%2B+B%5E2++=+%28A%5E2%2BB%5E2%29+-+2AB+ ALIGN=MIDDLE  ALT=\"+%28A-B%29%5E2++=+A%5E2+-+2AB+%2B+B%5E2++=+%28A%5E2%2BB%5E2%29+-+2AB+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5E2+=++3+%2B+sqrt%285%29+ ALIGN=MIDDLE  ALT=\"+A%5E2+=++3+%2B+sqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+B%5E2+=+3+-+sqrt%285%29+ ALIGN=MIDDLE  ALT=\"+B%5E2+=+3+-+sqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5E2+%2B+B%5E2++=++6+ ALIGN=MIDDLE  ALT=\"+A%5E2+%2B+B%5E2++=++6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2AB+=+-2%28sqrt%283%2Bsqrt%285%29%29%29+%2A+%28sqrt%283-sqrt%285%29%29%29++=+-2%28sqrt%289-5%29%29+=+-2%282%29+=+-4+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28A%5E2%2BB%5E2%29+-2AB+=+6-4+=+2+ ALIGN=MIDDLE  ALT=\"+%28A%5E2%2BB%5E2%29+-2AB+=+6-4+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Done. </SPAN>\n" );
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