Question

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

Answer 1

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,
`(dP)/(dx) =0`


`(dP)/(dx) =2x - 176=0 \\ \\ \Rightarrow2x=176 \\ \\ \Rightarrow x=88`

Thus, y = 88 - 176 = -88

Therefore, the two numbers are 88 and -88.