document.write( "Question 855358: If (a+b)²+(b+c)²+(c+d)²=4(ab+bc+cd), prove that a=b=c=d.\r
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Algebra.Com's Answer #515286 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(a+b)²+(b+c)²+(c+d)²=4(ab+bc+cd), \r\n" );
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document.write( "a²+2ab+b²+b²+2bc+c²+c²+2cd+d² = 4ab+4bc+4cd\r\n" );
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document.write( "Get 0 on the right by subtracting it from both sides:\r\n" );
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document.write( "a²-2ab+b²+b²-2bc+c²+c²-2cd+d² = 0\r\n" );
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document.write( "(a-b)²+(b-c)²+(c-d)² = 0\r\n" );
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document.write( "The three terms on the left are non-negative.\r\n" );
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document.write( "Thus they must all be 0.\r\n" );
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document.write( "Thus a-b=0, which means a=b.\r\n" );
document.write( "     b-c=0, which means b=c,\r\n" );
document.write( "     c-d=0, which means c=d\r\n" );
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document.write( "So a=b=c=d\r\n" );
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document.write( "Edwin
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