document.write( "Question 815452: if x*x+y*y=7xy, prove
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Algebra.Com's Answer #853720 by MathTherapy(10699)\"\" \"About 
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document.write( "if x*x+y*y=7xy, prove\r\n" );
document.write( "log(x+y)=1/2(logx+logy)+log3\r\n" );
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document.write( "If x*x+y*y=7xy, prove log(x+y)=1/2(logx+logy)+log3\r\n" );
document.write( "\"x%5E2+%2B+y%5E2+=+7xy\"   Prove: \r\n" );
document.write( "   \"%28x+%2B+y%29%5E2+=+x%5E2+%2B+2xy+%2B+y%5E2\" ----- Squaring x + y\r\n" );
document.write( "   \"%28x+%2B+y%29%5E2+=+x%5E2+%2B+y%5E2+%2B+2xy\"\r\n" );
document.write( "   \"%28x+%2B+y%29%5E2+=+7xy+%2B+2xy\" --- Substituting 7xy for \"x%5E2+%2B+y%5E2\" (GIVEN)\r\n" );
document.write( "   \"%28x+%2B+y%29%5E2+=+9xy\"\r\n" );
document.write( "\"sqrt%28%28x+%2B+y%29%5E2%29+=+sqrt%289xy%29\" ------- Taking the square root of both sides\r\n" );
document.write( "     \"x+%2B+y+=+3sqrt%28xy%29\" <=== ONLY the POSITIVE square root on the right-side is needed here \r\n" );
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document.write( "\"log+%28%28x+%2B+y%29%29+=+log+%28%283sqrt%28xy%29%29%29\" ----- Taking the log of both sides of the above equation\r\n" );
document.write( "\"log+%28%28x+%2B+y%29%29+=+log+%28%283%29%29+%2B+log+%28sqrt%28%28xy%29%29%29\"\r\n" );
document.write( "\"log+%28%28x+%2B+y%29%29+=+log+%28%283%29%29+%2B+log+%28%28xy%29%29%5E%281%2F2%29\"\r\n" );
document.write( "\"log+%28%28x+%2B+y%29%29+=+log+%28%283%29%29+%2B+%281%2F2%29log+%28%28xy%29%29\"\r\n" );
document.write( " <=== QED!
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