### ফাংশনের সমীকরণ বৈচিত্র্য

##### Score: 2 Points

Let $f(x) = x^2 + ax + b$. If for all nonzero real $x$, $f(x + \frac 1x)= f(x) + f(\frac1x)$ and the roots of $f(x) = 0$ are integers, what is the value of $a^2 + b^2$?
Source: Indian Math Olympiad

Algebra

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