document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065509>Question 1065509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (a - b)&sup2; = 5 and ab = 1, find the positive value of a + b.\r<BR>\n" );
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document.write( "I've successfully solved similar problems with addition of squares, but not a difference of squares. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #680682 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=680682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a-b)^2 = 5<BR>\n" );
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document.write( "take square root of both sides<BR>\n" );
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document.write( "1) a - b = square root(5)<BR>\n" );
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document.write( "2) ab = 1<BR>\n" );
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document.write( "solve equation 2 for a<BR>\n" );
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document.write( "a = 1/b<BR>\n" );
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document.write( "substitute for a in equation 1<BR>\n" );
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document.write( "(1/b) - b = square root(5)<BR>\n" );
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document.write( "b^2 +square root(5)b -1 = 0<BR>\n" );
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document.write( "use quadratic formula to find b<BR>\n" );
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document.write( "b = (-square root(5) + square root(5 + 4)) / 2 = (3 - square root(5)) / 2 = 0.382<BR>\n" );
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document.write( "a = 1 / ((3 - square root(5)) / 2) = 2 / (3 - square root(5)) = 2.618<BR>\n" );
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document.write( "a + b = 0.382 + 2.618 = 3<BR>\n" );
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