Question 1186502: If the sum of two numbers is 30. Find their maximum product.
Answer by greenestamps(13200)   (Show Source):
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Given the sum of two numbers, the product of the two numbers is greatest if the two numbers are the same.
Here is one way to show that using formal algebra.
The sum is 30, so let the two numbers be 15+x and 15-x; then their product is 225-x^2.
But x^2 is always 0 or positive, so the maximum value of 225-x^2 is when x is 0; that make the numbers 15+x and 15-x equal.
ANSWER: 15*15=225
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