document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179580>Question 1179580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers whose sum is  16  and  whose product is a maximum.   </SPAN>\n" );
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document.write( "To get a sum of 16, let the two numbers be 8-a and 8+a, where a is constant.<br><BR>\n" );
document.write( "The sum of the two numbers is 16; and the product is (8-a)(8+a)=64-a^2.<br><BR>\n" );
document.write( "The maximum value of 64-a^2 is when a=0, because a^2 is always non-negative.<br><BR>\n" );
document.write( "So the maximum value of the product is when a=0, making the two numbers 8-0=8 and 8+0=8.<br><BR>\n" );
document.write( "ANSWER: 8 and 8<br><BR>\n" );
document.write( "Note there is nothing special about the number 16 as the sum of the two numbers.  It is always true that for a given sum of two numbers, the maximum product of the two numbers is when they are equal.<br><BR>\n" );
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