Suppose r and s are the solutions of x^2 - 12x + 22 = 2x^2 + 22. Find r^2 + s^2.
+2498 First, let's rewrite the equation by moving all terms to one side:
2x^2 + 22 = x^2 - 12x + 22
Subtract x^2 and 22 from both sides:
x^2 + 12x = 0
Factor the left side:
x(x + 12) = 0
So, the solutions are x = 0 and x = -12, which are r and s. We can now find r^2 + s^2:
r^2 + s^2 = (0)^2 + (-12)^2 = 0 + 144 = 144
