Question

Among all pairs of numbers whose difference is 8, find a pair whose product is as small as possible. What is the minimum product?

Answer 1

x-y=8
x*(-8+x)
-8-x^2

Answer 2

x-y=8 implies x=8+y
P=xy=(8+y)y=8y+y^2
P'=8+2y
8+2y=0 implies y=-4 implies x=8-4=4

Answer 3

other than zero...
a-b = 8
a = 8+b
ab = (8+b)b
minimize b^2 + 8b
2b+8 = 0
2b = -8
b=-4

Answer 4

Thank you all very much. I am new to this site so this helps a lot. I'll have more questions throughout the next 24 hours.