If 1/a + 1/b = 7/8, and ab = 6, find both 'a' and 'b'.

Question

Please help me out here, I've been struggling with these problems. My math teachers says I don't need to use the quadratic formula for this, because you can just plug b for example when you solve for it on one of the equations.

Answer 1

1/a + 1/b = 7/8

(a + b) / ab = 7/8

(a + b) / 6 = 7/8

a + b = 42/8

a + b = 5.25

b = 5.25 - a

ab = 6

a(5.25 - a) = 6

5.25a - a^2 = 6

0 = a^2 - 5.25a + 6

Other than the quadratic formula, I see no other recourse.