Hello, help please

1) let $\displaystyle \tan\alpha$ and $\displaystyle \tan\beta $ roots of equation $\displaystyle x^2 + \pi x + \sqrt{2} = 0$ .

Evaluate : $\displaystyle A = \sin^2(\alpha+\beta) + \pi\sin(\alpha+\beta)\cos(\alpha+\beta) + \sqrt{2} \cos^2(\alpha+\beta)$

2) let $\displaystyle x,y,z > 0 $, prove that : $\displaystyle \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \geq x + y + z$

3) Find all function $\displaystyle f: \mathbb{R} \to \mathbb{R}$ such that : $\displaystyle f\left( xf(x) + f(y) \right ) = \left(f(x)\right)^2 +y$