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

 Apr 3, 2023
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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

 Apr 4, 2023

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