document.write( "Question 1111308: The difference of two positive numbers is six. Their product is 223 less than the sum of their squares. What are the two numbers?
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Algebra.Com's Answer #726293 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the larger number, y be the lesser number.\r\n" );
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document.write( "Then\r\n" );
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document.write( "x - y = 6,                (1)\r\n" );
document.write( "xy = x^2 + y^2 - 223.     (2)\r\n" );
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document.write( "Square equation (1) (both sides).  Keep equation (2) as is:\r\n" );
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document.write( "x^2 - 2xy + y^2 =  36,    (3)\r\n" );
document.write( "x^2 - xy  + y^2 = 223     (4)    (<<<---=== it is transformed eq(2) )\r\n" );
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document.write( "----------------------------------Subtract eq(3) from eq(4). You will get\r\n" );
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document.write( "      xy        = 187.\r\n" );
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document.write( "Now you have system of two equations\r\n" );
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document.write( "x - y =   6,\r\n" );
document.write( "xy    = 187.\r\n" );
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document.write( "It is reduced to the quadratic equation\r\n" );
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document.write( "x*(x-6) = 187\r\n" );
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document.write( "x^2 -6x - 187 = 0\r\n" );
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document.write( " =  = ,\r\n" );
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document.write( " =  = 17,   = 11.\r\n" );
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document.write( " =  = -11,   = -17.\r\n" );
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document.write( "Answer.  There are TWO solutions:   a) (x,y) = (17,11);  b) (x,y) = (-11,-17).      \r\n" );
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document.write( "         Since the problem asks about positive numbers, only first pair satisfies this requirement.\r\n" );
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