Question 90
Show that for any real $x \gt 0$ and integer $n \gt 0$ we have
$$
x^n + \frac{1}{x^n} - 2 \ge n^2 \left(x + \frac{1}{x} - 2\right).
$$
$$
x^n + \frac{1}{x^n} - 2 \ge n^2 \left(x + \frac{1}{x} - 2\right).
$$
MathNet 2013 Question 90
Math Olympiad Vault · MathNet 2013