Question

Suppose r and s are the solutions of x^2 − 12x + 22 = 0. Find r^2 + s^2

Answer 1

x² - 12x + 22 = 0

x² - 12x = -22

x² - 12x + 36 = 14

(x - 6)² = 14

x - 6 = +√14

x = 6 + √14

Let r = 6 - √14 and s = 6 + √14.

r² + s² = (6 - √14)² + (6 + √14)²

= 36 - 12√14 + 14 + 36 + 12√14 + 14

= 100