<s>[INST] Prove that $a + b + c + a^2 + b^2 + c^2 \leq4$ given that $a,b,c\geq-1$ and $a^3 + b^3 + c^3=1$ Let $a,b,c\geq-1$ be real numbers with $a^3 + b^3 + c^3=1$.
Prove that $$a + b + c + a^2 + b^2 + c^2 \leq4.$$ 
 [/INST] Hint:
This inequality is "separable" and it is enough to note that for $x> -1$,
$$f(x) = x^3-x^2-x+1 = (1+x)(1-x)^2 \geqslant 0$$ 
</s>