Question 59
Prove the inequality for every positive real number $a$ and every integer $n \geq 1$
$$
a^{n}+\frac{1}{a^{n}}-2 \geq n^{2}\left(a+\frac{1}{a}-2\right)
$$
and determine all cases in which the equal sign applies.
$$
a^{n}+\frac{1}{a^{n}}-2 \geq n^{2}\left(a+\frac{1}{a}-2\right)
$$
and determine all cases in which the equal sign applies.