document.write( "Question 1121203: if (2006-a)(2004-a)=2005, find (2006-a)^2 + (2004-a)^2.
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Algebra.Com's Answer #736991 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "From  (2006-a)(2004-a)=2005  you have\r\n" );
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document.write( "    2006*2004 - 2006a - 2004a + a^2 = 2005,\r\n" );
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document.write( "    2006*2004 - 2*2005*a + a^2 = 2005,\r\n" );
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document.write( "    -2*2005*a + a^2 = 2005 - 2006*2004.     (1)\r\n" );
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document.write( "Next,  \r\n" );
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document.write( "     (2006-a)^2 + (2004-a)^2 = 2006^2 -2*2006*a + a^2 + 2004^2 -2*2004*a + a^2 = \r\n" );
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document.write( "   = 2006^2 + 2004^2 -4*2005a + 2a^2 = 2006^2 + 2004^2 + (2*(-2*2005a  + a^2)) = \r\n" );
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document.write( "        Now replace the expression  (-2*2005a  + a^2)  by 2005 - 2006*2007, based on (1), and then you get\r\n" );
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document.write( "   = 2006^2 + 2004^2 + 2*(2005 - 2006*2004) = (2006-2004)^2 + 2*2005 = 2^2 + 4010 = 4014.\r\n" );
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document.write( "Answer.  4014.\r\n" );
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