document.write( "Question 1193027: What is the minimum product of two numbers whose difference is 5? What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #824974 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "What is the minimum product of two numbers whose difference is 5? What are the numbers?
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document.write( "Let x and y be the numbers; let x be the lesser number and y be the greater number, so y-x = 5.\r\n" );
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document.write( "Consider the mean value a =   and half the distance between x and y,  b =  =  = 2.5\r\n" );
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document.write( "Then, obviously,  x = a - 2.5  and  y = a + 2.5, so we can write\r\n" );
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document.write( "    xy = (a-2.5)*(a+2.5) = .\r\n" );
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document.write( "From this formula, it is clear that xy is minimum when a= 0, i.e. when x+y = 0;  in other words, the numbers x and y \r\n" );
document.write( "shoud be opposite: y = -x.\r\n" );
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document.write( "Thus we get that the minimum of the product xy  is achieved when x = -y.\r\n" );
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document.write( "Together with y-x = 5 it implies that y - (-y) = 5,  or  2y = 5, y = 5/2 = 2.5.\r\n" );
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document.write( "Thus the minimum value of xy is  at x= -2.5,  y= 2.5,  and the value of xy is   = -6.25 then.   \r\n" );
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document.write( "ANSWER.  The minimum is achieved when x= -2.5, y= 2.5.\r\n" );
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document.write( "         The minimum value of the product is  then -6.25.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There are many different ways and methods of solving such problems.\r
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\n" ); document.write( "\n" ); document.write( "They differ in the level of necessary prerequisites, which the reader should know to understand the solution.\r
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\n" ); document.write( "\n" ); document.write( "What I exposed here, is traditionally considered in Math and in Math popular literature as \r
\n" ); document.write( "\n" ); document.write( "the SIMPLEST method of solving, accessible for students with minimal level of knowledge (for the most young readers).\r
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