Question 23
a and b are positive real numbers. $x_i$ are real numbers lying between $a$ and $b$. Show that
$$(x_1 + x_2 + \ldots + x_n)\left(\frac{1}{x_1} + \frac{1}{x_2} + \ldots + \frac{1}{x_n}\right) \leq \frac{n^2 (a + b)^2}{4ab}.$$
$$(x_1 + x_2 + \ldots + x_n)\left(\frac{1}{x_1} + \frac{1}{x_2} + \ldots + \frac{1}{x_n}\right) \leq \frac{n^2 (a + b)^2}{4ab}.$$