document.write( "Question 1027521: If the sum of two numbers is 32 what will be the largest possible value of their product \n" ); document.write( "

Algebra.Com's Answer #642735 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "If the sum of two numbers is 32 what will be the largest possible value of their product
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document.write( "Let x be one of the two numbers.\r\n" );
document.write( "Then the other number is  (32-x),  and the product of the two numbers is   = .\r\n" );
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document.write( "To answer the question, complete the square in the right side quadratic polynomial.\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "Now, the right side has the maximum equal to   =   at  x = 16.\r\n" );
document.write( "For any other value of  x  the negative quadratic term in the right side of the expression makes it lesser.\r\n" );
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document.write( "So, the maximum of the product of the numbers  x  and  (32-x)  is achieved at  x = 16  and it is  256.\r\n" );
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