SOLUTION: Two numbers have a difderence of 8. Find the numbers so that the square of the larger minus double the smaller gives the minimum possible result
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Question 1079711: Two numbers have a difderence of 8. Find the numbers so that the square of the larger minus double the smaller gives the minimum possible result Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! Let the two numbers be a and b
Given: a - b = 8 [a is the larger number]
Need to minimize the expression a^2 - 2b -> a^2 - 2(a-8) -> a^2 - 2a + 16
Take the derivative and set equal to zero:
2a - 2 = 0 -> a = 1
So the minimum result is obtained if a = 1 and b = -7
The graph of a^2 - 2a + 16 has a minimum at a = 1, so the answer is correct.
