prove

[ertyu]

1.Let $ z \in {C^ * } $such that $\left| {{z^3} + \frac{1}{{{z^3}}}} \right| \le 2$. prove that $\left| {z + \frac{1}{z}} \right| \le 2$

2.Find all non-negative numbers x, y, z, such that .
$\sqrt{x-y+z}=\sqrt{x}-\sqrt{y}+\sqrt{z}$

3. Solve the following equation

[Руст]

1. Let $z+\frac 1z=re^{i\phi}$, then $|z^3+z^{-3}|=|r^3e^{i3\phi}+3re^{i\phi}|\ge r(r^2-3)> 2$ if $r>2$.

2. It is true, if $x=y$ or $y=z$.

3. $x=3$ is solution. If $x>3$ right side $<1<x-2$. If $x<3$ right side $>1>x-2$.