document.write( "Question 424577: Find 2 numbers whose sum is 40 if the sum of their squares is to be a minimum. What is the minimum? \n" ); document.write( "

Algebra.Com's Answer #295936 by richard1234(7193) $\"\"$ $\"About$

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We have two numbers, $\"a\"$ and $\"40-a\"$ and want to minimize the sum $\"a%5E2+%2B+%2840-a%29%5E2\"$ , or $\"2a%5E2+-+80a+%2B+1600\"$ . The parabola's leading coefficient is positive, so the minimum value occurs at the \"vertex,\" which occurs when $\"a+=+80%2F%282%282%29%29+=+20\"$ . Thus, {20,20} minimizes the sum and this sum is $\"20%5E2+%2B+20%5E2+=+800\"$ . \n" ); document.write( "

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