The sum of a number and 18 times its reciprocal is 9. Find the​ number(s).

Question

Find the reciprocal of x.

Answer 1

n + 18*(1/n) = 9 (The problem)

n^2 + 18 = 9n (Multiply both sides by n)

n^2 -9n + 18 = 0

n = (-(-9) ± √(81-72)) / 2 (Quadratic formula)

n = 6 and 3

Do the answers check? Yes.

Answer 2

From the information if x is the unknown number

x + 1/x = 9 or x² + 18 = 9x or x² -9x + 18 = 0

This factors as (x-6)(x-3) = 0 So, x = 6 & 3 are the solutions.