document.write( "Question 1118976: Find two numbers such that the smaller subtracted from the larger is 3 and the difference of the square of the larger subtracted from square of the smaller is 45. \n" ); document.write( "

Algebra.Com's Answer #734405 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find two numbers such that the smaller subtracted from the larger is 3 and
\n" ); document.write( "the difference of the square of the larger subtracted from square of the smaller is 45.
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document.write( "You are given\r\n" );
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document.write( "x - y = 3           (1)    (where x is the larger number)\r\n" );
document.write( "y^2 - x^2 = 45.     (2)\r\n" );
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document.write( "From eq(2), you have\r\n" );
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document.write( "(y-x)*(x+y) = 45.\r\n" );
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document.write( "Replace (y-x) in the left side by -3, based on eq(1). You will get\r\n" );
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document.write( "-3*(x+y) = 45,   or\r\n" );
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document.write( "x + y = -45/3 = -15.\r\n" );
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document.write( "Thus you have two equatiuons\r\n" );
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document.write( "x - y =   3,      (1)\r\n" );
document.write( "x + y = -15       (3)    <<<---=== you were fortune to reduce the given system with a quadratic equation to system of two linear equations !\r\n" );
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document.write( "Add them to get  2x = 3+(-15) = -12  ====>  x = -12/2 = -6.\r\n" );
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document.write( "Then from eq(1),  y = x - 3 = -6-3 = -9.\r\n" );
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document.write( "Answer.  The numbers are  -6 and -9.\r\n" );
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document.write( "Check.   (-9)^2 - (-6)^2 = 81 - 36 = 45.     ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Be aware: the answer by @josgarithmetic \"6 and 9\" is INCORRECT !\r
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