document.write( "Question 815452: if x*x+y*y=7xy, prove
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Algebra.Com's Answer #490983 by Edwin McCravy(20059)\"\" \"About 
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if x*x+y*y=7xy, prove
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document.write( "     x²+y² = 7xy     <--given\r\n" );
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document.write( "The left side would be a perfect square if it had\r\n" );
document.write( "2xy between the x² and y².  So we add 2xy to both\r\n" );
document.write( "sides to make it into a perfect square:\r\n" );
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document.write( " x²+2xy+y² = 7xy+2xy\r\n" );
document.write( "(x+y)(x+y) = 9xy\r\n" );
document.write( "    (x+y)² = 9xy\r\n" );
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document.write( "Take positive square roots of both sides\r\n" );
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document.write( "   √(x+y)² = √9xy\r\n" );
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document.write( "       x+y = √9xy\r\n" );
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document.write( "       x+y = 3√xy\r\n" );
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document.write( "Take logs of both sides:\r\n" );
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document.write( "     log(x+y) = log(3√xy)\r\n" );
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document.write( "     log(x+y) = log(3) + log(√xy)\r\n" );
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document.write( "     log(x+y) = log(3) + log(√x√y)\r\n" );
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document.write( "     log(x+y) = log(3) + log(√x) + log(√y)\r\n" );
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document.write( "Change square roots to 1/2 powers:\r\n" );
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document.write( "     log(x+y) = log(3) + log(x1/2) + log(y1/2)\r\n" );
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document.write( "Move eponents in front as multipliers:\r\n" );
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document.write( "     log(x+y) = log(3) + (1/2)log(x) + (1/2)log(y)\r\n" );
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document.write( "Foctor out (1/2) from the last two terms:\r\n" );
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document.write( "     log(x+y) = log(3) + (1/2)[log(x) + log(y)]\r\n" );
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document.write( "Rearrange the terms to what we were to prove:\r\n" );
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document.write( "     log(x+y) = (1/2)[log(x) + log(y)] + log(3) \r\n" );
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document.write( "Edwin
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