Proving inequalities hold for all values

Question

Show that the inequality

$$\frac st + \frac tr + \frac rs \ge 3$$

holds for all positive $r,s$ and $t$.

Use AM GM inequality – lab bhattacharjee Oct 02 '14 at 15:24 — lab bhattacharjee, Oct 02 '14 at 15:24

score 3 · Accepted Answer · answered Oct 02 '14 at 15:25

3

Since $s/t,t/r,r/s\gt 0$,

$$\frac st+\frac tr+\frac rs\ge 3\sqrt[3]{\frac st\cdot \frac tr\cdot\frac rs}=3.$$

answered Oct 02 '14 at 15:25

mathlove

1 Answers1