document.write( "Question 647301: x^2+y^2+z^2- xy -yz-zx-yz=0 then prove that x=y=z
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Algebra.Com's Answer #406138 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x² + y² + z² - xy - yz - zx - yz = 0 then prove that x = y = z\r\n" );
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document.write( "That isn't true. For here is a counter-example:\r\n" );
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document.write( "x = 0, y = 1, z = 1\r\n" );
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document.write( "0² + 1² + 1² - 0y - 1·1 - 1·0 - 1·1 = 0\r\n" );
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document.write( "0 +  1  + 1  -  0 -   1 -   0 -   1 = 0\r\n" );
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document.write( "                                  0 = 0\r\n" );
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document.write( "Maybe there was a typo, since there are two like \r\n" );
document.write( "terms -yz and -yz that immediately combine to give -2yz.\r\n" );
document.write( "It seems strange that as advanced a problem as this would\r\n" );
document.write( "leave something undone as elementary as requiring two like terms\r\n" );
document.write( "to be combined.  Thus I suspect there was a typo.  If so,\r\n" );
document.write( "you can correct it in the thank-you note.\r\n" );
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document.write( "Edwin
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