If 1/a + 1/b = 7 and ab = 1/4 , find 1/a^2 + 1/b^2

Question

don’t solve for a and b specifically, just solve for: 1/a^2 + 1/b^2

algebra 2

Answer 1

(1/a) + (1/b) = 7

(1/a)² + [2/(ab)] + (1/b)² = 49

(1/a)² + (1/b)² = 49 -[2/(ab)] = 49-8 = 41