document.write( "Question 994122: Please help me solve this equation\r
\n" ); document.write( "\n" ); document.write( "If x^2 + 2xy = 40 and y^2 + 1/2xy = 15 find x^2 + y^2
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Algebra.Com's Answer #613333 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "x^2 + 2xy = 40,       (1)\r\n" );
document.write( "y^2 + 1/2xy = 15.     (2)\r\n" );
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document.write( "Multiply the second equation by 4 (both sides). You will have an equivalent system\r\n" );
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document.write( "x^2 + 2xy = 40,       (3)\r\n" );
document.write( "4y^2 + 2xy = 60.      (4)\r\n" );
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document.write( "Now add equations (3) and (4) of the last system. You will get\r\n" );
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document.write( " = , or  = , or  = , or x + 2y = +/-10.      (5)\r\n" );
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document.write( "Next, distract the equation (4) from the equation (3). You will get\r\n" );
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document.write( " = , or (x+2y)*(x-2y) = 20.                 (6)\r\n" );
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document.write( "By combining (5) and (6), you have two linear systems of two equations in two unknowns\r\n" );
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document.write( ",        and     .\r\n" );
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document.write( "First of these two systems has the solution x=6, y=2.\r\n" );
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document.write( "The second system has negative solutions x=-6, y=-2.\r\n" );
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document.write( "According to the condition, only the pair x=6, y=2 does suit. \r\n" );
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