document.write( "Question 1209654: Find the unique pair of real numbers (x,y) satisfying
\n" ); document.write( "(6x^2 - 18x + 17) + (3y^2 + 6y + 11) = 28
\n" ); document.write( "and x + y = 20.\r
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\n" ); document.write( "\n" ); document.write( "Enter your answer as an ordered pair in the format $(x,y)$, where $x$ and $y$ are replaced by appropriate numbers. \n" ); document.write( "

Algebra.Com's Answer #849780 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Find the unique pair of real numbers (x,y) satisfying
\n" ); document.write( "(6x^2 - 18x + 17) + (3y^2 + 6y + 11) = 28
\n" ); document.write( "and x + y = 20.
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\n" ); document.write( "\n" ); document.write( "        In the post by @CPhill, the final answer is {(8,12)}.\r
\n" ); document.write( "\n" ); document.write( "        This answer CONTRADICTS to what is written in his post before it, and is factually INCORRECT.\r
\n" ); document.write( "\n" ); document.write( "        Also, his post is full of non-necessary calculations.\r
\n" ); document.write( "\n" ); document.write( "        Below I present my solution, which is much shorter, simple and straightforward.\r
\n" ); document.write( "\n" ); document.write( "        At the end, I will provide a correct answer.\r
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document.write( "Starting equation is\r\n" );
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document.write( "    (6x^2 - 18x + 17) + (3y^2 + 6y + 11) = 28.\r\n" );
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document.write( "Simplify by combining like terms\r\n" );
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document.write( "    6x^2 - 18x + 3y^2 + 6y = 28 - 17 - 11,\r\n" );
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document.write( "    6x^2 - 18x + 3y^2 + 6y = 0.\r\n" );
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document.write( "Now divide both sides by 3\r\n" );
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document.write( "    2x^2 - 6x + y^2 + 2y = 0.\r\n" );
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document.write( "Substitute here y = 20-x from the second given equation\r\n" );
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document.write( "    2x^2 - 6x + (20-x)^2 + 2*(20-x) = 0,\r\n" );
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document.write( "    2x^2 - 6x + 400 - 40x + x^2 + 40 - 2x = 0,\r\n" );
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document.write( "    3x^2 - 48x + 440 = 0.\r\n" );
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document.write( "The discriminant of this quadratic equation is negative\r\n" );
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document.write( "    d = b^2 - 4ac = (-48)^2 - 4*3*440 = -2976,\r\n" );
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document.write( "which means that equation (2) has no solution.\r\n" );
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\n" ); document.write( "\n" ); document.write( "ANSWER. There is $\"highlight%28highlight%28NO%29%29\"$ such pair of real numbers, satisfying the given conditions.\r
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\n" ); document.write( "\n" ); document.write( "As presented in the post, the problem is posed INCORRECTLY.\r
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\n" ); document.write( "\n" ); document.write( "It requests to find something that does not exist in the nature,
\n" ); document.write( "contradicts to Math and can not be found.\r
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