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Reptile [31]
3 years ago
15

Find two numbers whose difference is 176 and whose product is a minimum.

Mathematics
1 answer:
Zanzabum3 years ago
8 0
Let the two required numbers be x and y, then x - y = 176, thus y = x - 176.

Let the product of the two numbers be represented by

P = xy x(x - 176) = x^2 - 176x

For the product to be minimum, \frac{dP}{dx} =0

\frac{dP}{dx} =2x - 176=0 \\  \\ \Rightarrow2x=176 \\  \\ \Rightarrow x=88

Thus, y = 88 - 176 = -88

Therefore, the two numbers are 88 and -88.
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==========================================================

Work Shown:

The first term is a_1 = 24 and we go up by 7 each time.
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