document.write( "Question 39164: The sum of 2 numbers is 25. The sum of their squares is 313. Find the two numbers...thank you! \n" ); document.write( "
Algebra.Com's Answer #24601 by AnlytcPhil(1806)\"\" \"About 
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The sum of 2 numbers is 25. The sum of their squares is 313. Find the two numbers...thank you>...The sum of 2 numbers is 25...<<\r\n" );
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document.write( "x + y = 25\r\n" );
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document.write( ">>...The sum of their squares is 313...<<\r\n" );
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document.write( "x² + y² = 313\r\n" );
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document.write( "So you have the system of equations:\r\n" );
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document.write( "x + y = 25\r\n" );
document.write( "x² + y² = 313\r\n" );
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document.write( "To solve by substitution:\r\n" );
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document.write( "Solve the first equation for y\r\n" );
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document.write( "y = 25 - x\r\n" );
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document.write( "Substityte (25 - x) for y in \r\n" );
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document.write( "x² + y² = 313\r\n" );
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document.write( "x² + (25 - x)² = 313\r\n" );
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document.write( "x² + (625 - 50x + x²) = 313\r\n" );
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document.write( "x² + 625 - 50x + x² = 313\r\n" );
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document.write( "2x² - 50x + 625 = 313\r\n" );
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document.write( "2x² - 50x + 625 = 313\r\n" );
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document.write( "2x² - 50x + 312 = 0\r\n" );
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document.write( "2(x² - 25x + 156) = 0\r\n" );
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document.write( "Factor: two integers which multiply to give 156 and add to give 25\r\n" );
document.write( "are 13 and 12.\r\n" );
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document.write( "2(x - 13)(x - 12) = 0\r\n" );
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document.write( "Set each factor = 0 and solve:\r\n" );
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document.write( "x - 13 = 0 gives x = 13\r\n" );
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document.write( "x - 12 = 0 gives x = 12\r\n" );
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document.write( "Then substitute each of these in \r\n" );
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document.write( "y = 25 - x\r\n" );
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document.write( "Substituting x = 13\r\n" );
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document.write( "y = 25 - 13\r\n" );
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document.write( "y = 12\r\n" );
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document.write( "So one solution is (x, y) = (13, 12)\r\n" );
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document.write( "Substituting x = 12\r\n" );
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document.write( "y = 25 - 12\r\n" );
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document.write( "y = 13\r\n" );
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document.write( "So one solution is (x, y) = (12, 13)\r\n" );
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document.write( "Either way the two numbers are 12 and 13.\r\n" );
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document.write( "Edwin
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