Question 60
Let $a$, $b$ be two positive real numbers and $n$ be an integer greater than $1$. Prove that for all positive real number $x$ satisfying $x^n \leq a x + b$, we have
$$
x \lt n^{-1/2} \sqrt{a} + n^{1/2} \sqrt{b}.
$$
$$
x \lt n^{-1/2} \sqrt{a} + n^{1/2} \sqrt{b}.
$$