Writing It Up · Superchallenge problem

$\dfrac ab + \dfrac ba \ge 2$

$\dfrac{a + b}{2} \ge \sqrt{ab}$ whenever $ab > 0$

$\dfrac{a^2}{b^2} + \dfrac{b^2}{a^2} \ge 2$

$(a + b)\left(\dfrac1a + \dfrac1b\right) \ge 4$