document.write( "Question 41589: One positive number is 8 more than another. The sum of their squares is 130. Find both numbers. \n" ); document.write( "

Algebra.Com's Answer #26864 by AnlytcPhil(1806) $\"\"$ $\"About$

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One positive number is 8 more than another.\r\n" );
document.write( "The sum of their squares is 130.  Find both numbers.\r\n" );
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document.write( "Let one positive number = x\r\n" );
document.write( "Let another positive number = y\r\n" );
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document.write( ">>...One positive number is 8 more than another...<<\r\n" );
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document.write( "So                    x = y + 8\r\n" );
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document.write( ">>...The sum of their squares is 130...<<\r\n" );
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document.write( "So                  x² + y² = 130      \r\n" );
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document.write( "We have the system of equations\r\n" );
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document.write( "x = y + 8\r\n" );
document.write( "x² + y² = 130\r\n" );
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document.write( "Substitute (y + 8) from the first for x in the second\r\n" );
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document.write( "           (y + 8)² + y² = 130\r\n" );
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document.write( "     (y + 8)(y + 8) + y² = 130\r\n" );
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document.write( "  y² + 8y + 8y + 64 + y² = 130\r\n" );
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document.write( "            2y² + 16y + 64 = 130\r\n" );
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document.write( "            2y² + 16y - 66 = 0\r\n" );
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document.write( "           2(y² + 8y - 33) = 0\r\n" );
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document.write( "          2(y + 11)(y - 3) = 0   \r\n" );
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document.write( "Set each variable factor = 0\r\n" );
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document.write( "        y + 11 = 0 gives y = -11\r\n" );
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document.write( "         y - 3 = 0 gives y = 3\r\n" );
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document.write( "Discard the negative answer\r\n" );
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document.write( "Substitute 3 for y in \r\n" );
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document.write( "             x = y + 8\r\n" );
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document.write( "             x = 3 + 8\r\n" );
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document.write( "             x = 11\r\n" );
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document.write( "So the numbers are 11 and 3\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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