document.write( "Question 504161: solving max/min problems: the sum of two positive number is 56.Find the two numbers,if their product ia amaximum. \n" ); document.write( "

Algebra.Com's Answer #339528 by Earlsdon(6294) $\"\"$ $\"About$

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If the two numbers are a and b, then a+b = 56 which can be written as a = 56-b.
\n" ); document.write( "Now a*b must be a maximum (call it y)so we can write a*b as:
\n" ); document.write( " $\"y+=+%2856-b%29%2Ab\"$ Simplify.
\n" ); document.write( " $\"y+=+56b-b%5E2\"$ This is a quadratic equation and the graph will be a parabola opening downward.
\n" ); document.write( "So all you need to do to find the maximum is find the value of b at the point of the parabola's vertex which is given by:
\n" ); document.write( " $\"b+=+-56%2F2%28-1%29\"$
\n" ); document.write( " $\"b+=+28\"$
\n" ); document.write( "So the two numbers are: a = 28 and b = 28.
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