Question

Find two numbers whose difference is 154 and whose product is a minimum.

Answer 1

Y - x = 154
let z = xy = x(154 + x) = x^2 + 154x

we need to find the minimum value of z

z' =   2x + 154  which = zero for minm or maxm value

x = -77   and y = 154 -77 = 77

so the 2 numbers are -77 and 77