document.write( "Question 1209168: Find all ordered pairs (x,y) of real numbers such that x + y = 10 and x^2 + y^2 = 62 + 2xy.\r
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Algebra.Com's Answer #847776 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "I will re-formulate the problem in normal human mathematical language,
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\n" ); document.write( "\n" ); document.write( "         Find all real solutions to this system of equations
\n" ); document.write( "             x + y = 10                            (1)
\n" ); document.write( "             x^2 + y^2 = 62 + 2xy.         (2)
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document.write( "Transform second equation this way\r\n" );
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document.write( "    x^2 - 2xy + y^2 = 62,\r\n" );
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document.write( "    (x-y)^2 = 62,\r\n" );
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document.write( "    |x-y| = .\r\n" );
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document.write( "Then the given system of equations takes the form\r\n" );
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document.write( "    x + y = 10,\r\n" );
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document.write( "    x - y = +/- .\r\n" );
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document.write( "It falls apart in two systems of equations.  First system is\r\n" );
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document.write( "    x + y = 10,\r\n" );
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document.write( "    x - y = .\r\n" );
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document.write( "By adding equations, you will get\r\n" );
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document.write( "    2x = 10 +   --->  x = 5 + ,\r\n" );
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document.write( "By subtracting equations, you will get\r\n" );
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document.write( "    2y = 10 -   --->  y = 5 - .\r\n" );
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document.write( "Second system of equations is\r\n" );
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document.write( "    x + y = 10,\r\n" );
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document.write( "    x - y = .\r\n" );
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document.write( "By adding equations, you will get\r\n" );
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document.write( "    2x = 10 -   --->  x = 5 - ,\r\n" );
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document.write( "By subtracting equations, you will get\r\n" );
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document.write( "    2y = 10 +   --->  y = 5 + .\r\n" );
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document.write( "ANSWER.  There are two solutions:  (x,y) = (,)\r\n" );
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document.write( "                             and   (x,y) = (,).\r\n" );
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