document.write( "Question 1065509: If (a - b)² = 5 and ab = 1, find the positive value of a + b.\r
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\n" ); document.write( "I've successfully solved similar problems with addition of squares, but not a difference of squares. \n" ); document.write( "

Algebra.Com's Answer #680700 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "If (a - b)^2 = 5 and ab = 1, find the positive value of a + b.
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document.write( "If (a-b)^2 = 2, then a^2 - 2ab + b^2 = 5.\r\n" );
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document.write( "Hensce,  a^2 + 2ab + b^2 = (a^2 - 2ab + b^2) + 4ab = 5 + 4 = 9.\r\n" );
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document.write( "In other words, (a+b)^2 = 9.\r\n" );
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document.write( "Then a + b = 3.\r\n" );
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document.write( "It is the same as the Fombitz' solution, but more straightforward.\r\n" );
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