gaokao 2011 Q16

gaokao · China · shanghai-arts Inequalities Identify Always-True Inequality from Options
16. If $a, b \in \mathbb{R}$ and $ab > 0$, then which of the following inequalities always holds?
(A) $a^2 + b^2 > 2ab$
(B) $a + b \geq 2\sqrt{ab}$
(C) $\frac{1}{a} + \frac{1}{b} > \frac{2}{\sqrt{ab}}$
(D) $\frac{b}{a} + \frac{a}{b} \geq 2$
16. If $a, b \in \mathbb{R}$ and $ab > 0$, then which of the following inequalities always holds?\\
(A) $a^2 + b^2 > 2ab$\\
(B) $a + b \geq 2\sqrt{ab}$\\
(C) $\frac{1}{a} + \frac{1}{b} > \frac{2}{\sqrt{ab}}$\\
(D) $\frac{b}{a} + \frac{a}{b} \geq 2$