Proof the inequality for some real numbers $a$, $b$: $$\frac{1}{\sqrt{a^2+a+1}}+\frac{1}{\sqrt{b^2+b+1}}+\frac{4}{\sqrt{(a+b)^2-2(a+b)+4}} \leq 4$$
My idea was: $(0+0+1)(a^2+a+1)\geq 1$ (CBS) and $(0+0+1)(b^2+b+1)\geq 1$ (CBS)
But I don't know if that is correct. Please help. :)