<s>[INST] If $a^3 + b^3 +3ab = 1$, find $a+b$ 
Given that the real numbers $a,b$ satisfy $a^3 + b^3 +3ab = 1$, find $a+b$.

I tried to factorize it but unable to do it.
 [/INST] The three solutions of the equation $a^3+b^3+3ab=1$ are 
$$b_1=1-a,$$
$$b_2,b_3 = \frac{1}{2}\left(a-1\pm i\sqrt{3}(1+a)\right).$$
If $a\neq -1$, since $a,b\in\mathbb{R}$, we must have $a+b=a+b_1=1$. If 
$a=-1$, then the imaginary part of $b_2,b_3$ vanishes and we find two solutions for $(a,b)$: $(-1,-1)$ and $(-1,2)$ so $a+b$ is -2 or 1 respectively.
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