document.write( "Question 1133746: the squarqe of the sum of two numbers is 144 and the sum of their squares is 80. find the number \n" ); document.write( "
Algebra.Com's Answer #750989 by Edwin McCravy(20060)\"\" \"About 
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\"system%28%28x%2By%29%5E2=144%2Cx%5E2%2By%5E2=80%29\"\r\n" );
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document.write( "\"system%28x%5E2%2B2xy%2By%5E2=144%2Cx%5E2%2By%5E2=80%29\"\r\n" );
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document.write( "Subtract the two equations:\r\n" );
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document.write( "\"%28x%5E2%2B2xy%2By%5E2%29-%28x%5E2%2By%5E2%29=144-80\"\r\n" );
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document.write( "\"x%5E2%2B2xy%2By%5E2-x%5E2-y%5E2=64\"\r\n" );
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document.write( "\"2xy=64\"\r\n" );
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document.write( "\"xy=32\"\r\n" );
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document.write( "\"y=32%2Fx\"\r\n" );
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document.write( "Substitute in the original equation:\r\n" );
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document.write( "\"x%5E2%2By%5E2=80\"\r\n" );
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document.write( "\"x%5E2%2B%2832%2Fx%29%5E2=80\"\r\n" );
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document.write( "\"x%5E2%2B1024%2Fx%5E2=80\"\r\n" );
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document.write( "\"x%5E4%2B1024=80x%5E2\"\r\n" );
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document.write( "\"x%5E4-80x%5E2%2B1024=0\"\r\n" );
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document.write( "\"%28x%5E2-16%29%28x%5E2-64%29=0\"\r\n" );
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document.write( "\"%28x-4%29%28x%2B4%29%28x-8%29%28x%2B8%29=0\"\r\n" );
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document.write( "x-4=0; x+4=0; x-8=0; x+8=0\r\n" );
document.write( "  x=4;   x=-4;  x=8;   x=-8\r\n" );
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document.write( "Substitute each in {{y=32/x}}}\r\n" );
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document.write( "\"y=32%2F4\";\"y=32%2F%28-4%29\"; \"y=32%2F8\"; \"y=32%2F%28-8%29\"\r\n" );
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document.write( "\"y=8\";\"y=-8\"; \"y=4\"; \"y=-4\"\r\n" );
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document.write( "Solutions are\r\n" );
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document.write( "(x,y)=(4,8), (-4,-8), (8,4), (-8,-4)\r\n" );
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document.write( "Edwin
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