Question 100
Let $x$ and $y$ be positive real numbers.
a) Prove: if $x^{3}-y^{3} \geq 4 x$, then $x^{2}\gt 2 y$.
b) Prove: if $x^{5}-y^{3} \geq 2 x$, then $x^{3} \geq 2 y$.
a) Prove: if $x^{3}-y^{3} \geq 4 x$, then $x^{2}\gt 2 y$.
b) Prove: if $x^{5}-y^{3} \geq 2 x$, then $x^{3} \geq 2 y$.