document.write( "Question 1092290: the difference of two numbers is 24. Find the two numbers if their product is to be a minimum. \n" ); document.write( "

Algebra.Com's Answer #706894 by ikleyn(52884) $\"\"$ $\"About$

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document.write( "x - y = 24,\r\n" );
document.write( "xy  ---->  min.\r\n" );
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document.write( "It is the same as to find the minimum of the quadratic function x*(x-24), or, which is the same, of the quadratic function .\r\n" );
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document.write( "The roots of the function are at 0 and 24; therefore, the minimum is at  the middle point  x =  = 12.\r\n" );
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document.write( "Then y = 12-24 = -12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The numbers are 12 and - 12.\r
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\n" ); document.write( "\n" ); document.write( "See the plot below as an illustration.\r
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\n" ); document.write( "\n" ); document.write( "Plot y = x*(x-24)\r
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