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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!

 Apr 4, 2021
 #1
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$\alpha^2 + \beta^2 = \boxed{5}$

 Apr 4, 2021
 #2
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Please show your work, how did you even get that answer?

Guest Apr 4, 2021

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