Suppose r and s are the solutions of x^2 − 12x + 22 = 0. Find r^2 + s^2 .
Explain solution
By the quadratic formula, the roots of x^2 - 12x + 22 = 0 are 6 + sqrt(18) and 6 - sqrt(18).
Then r^2 + s^2 = (6 + sqrt(18))^2 + (6 - sqrt(18))^2
= 36 + 12 sqrt(18) + 18 + 36 - 12 sqrt(18) + 18
= 108
actually its 100 according to Vieta's formulas
