The function f : \(\mathbb{R} \to \mathbb{R} \) satisfies \(x^2 f(x) + f(1 - x) = -x^4 + 2x\) for all real numbers x. Then f(x) can be uniquely determined for all values of x, except \(f(\alpha)\) and \(f(\beta)\) for some real numbers \(\alpha\) and \(\beta\). Compute \(\alpha^2 + \beta^2.\)
Thanks so much!
