document.write( "Question 1062388: x+y=x×y=x²-y² \n" ); document.write( "
Algebra.Com's Answer #677267 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "x+y = x×y = x²-y²\r\n" );
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document.write( "Obviously x = 0 = y is a solution.\r\n" );
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document.write( "if x+y = x²-y² then\r\n" );
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document.write( "\"x%2By\"\"%22%22=%22%22\"\"x%5E2-y%5E2\"\r\n" );
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document.write( "\"x%2By\"\"%22%22=%22%22\"\"%28x-y%29%28x%2By%29\"\r\n" );
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document.write( "\"%28x%2By%29-%28x-y%29%28x%2By%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"%28x%2By%29%281-%28x-y%29%5E%22%22%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"%28x%2By%29%281-x%2By%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"x%2By=0\"; \"1-x%2By=0\"\r\n" );
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document.write( "\"y=-x\";   \"y=x-1\"\r\n" );
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document.write( "But we have to make sure that\r\n" );
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document.write( "\"x%2By=xy\"\r\n" );
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document.write( "For the first case \"y=-x\"\r\n" );
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document.write( "\"x-x=x%28-x%29\"\r\n" );
document.write( "\"0=x%5E2\"\r\n" );
document.write( "\"0=x\"\r\n" );
document.write( "\"y=-x\"\r\n" );
document.write( "\"y=0\"\r\n" );
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document.write( "So one solution is x = y = 0, the obvious one.\r\n" );
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document.write( "------------------\r\n" );
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document.write( "For the second case \"y=x-1\"\r\n" );
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document.write( "\"y=x-1\"\r\n" );
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document.write( "\"x%2By=xy\"\r\n" );
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document.write( "\"x%2B%28x-1%29=x%28x-1%29\"\r\n" );
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document.write( "\"x%2Bx-1=x%5E2-x\"\r\n" );
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document.write( "\"2x-1=x%5E2-x\"\r\n" );
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document.write( "\"0=x%5E2-3x%2B1\"\r\n" );
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document.write( "\"x%5E2-3x%2B1=0\"\r\n" );
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document.write( "\"x+=+%28-%28-3%29+%2B-+sqrt%28%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+\"\r\n" );
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document.write( "\"x+=+%283+%2B-+sqrt%289-4%29%29%2F2+\"\r\n" );
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document.write( "\"x+=+%283+%2B-+sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "\"y=x-1\"\r\n" );
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document.write( "For \"x+=+%283+%2B+sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "\"y=+%283+%2B+sqrt%285%29%29%2F2-1\"\r\n" );
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document.write( "\"y=+%283+%2B+sqrt%285%29%29%2F2-2%2F2\"\r\n" );
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document.write( "\"y=+%281+%2B+sqrt%285%29%29%2F2\"\r\n" );
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document.write( "So a second solution is:\r\n" );
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document.write( "\"x+=+%283+%2B+sqrt%285%29%29%2F2+\", \"y=+%281+%2B+sqrt%285%29%29%2F2\" \r\n" );
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document.write( "----------------\r\n" );
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document.write( "For \"x+=+%283+-+sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "\"y=+%283+-+sqrt%285%29%29%2F2-1\"\r\n" );
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document.write( "\"y=+%283+-+sqrt%285%29%29%2F2-2%2F2\"\r\n" );
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document.write( "\"y=+%281+-+sqrt%285%29%29%2F2\"\r\n" );
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document.write( "So a third solution is:\r\n" );
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document.write( "\"x+=+%283+-+sqrt%285%29%29%2F2+\", \"y=+%281+-+sqrt%285%29%29%2F2\" \r\n" );
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document.write( "Edwin
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