Suppose that ab = 7 and a^2b + ab^2 + a+b = 80. What is a^2+b^2?

Answer 1

a^2b + ab^2 = ab(a+b)
so, we have

ab(a+b) + (a+b) = 80
7(a+b) + (a+b) = 80
8(a+b) = 80
(a+b) = 10

(a+b)^2 = a^2+2ab+b^2
a^2+b^2 = (a+b)^2 - 2ab = 100-14 = 86