Question 102
Show that, if $a, b, c \in (0, \infty)$ and $a + b + c = 3$, then
$$
a^5 + b^5 + c^5 + 8(ab + bc + ca) \ge 27.
$$
$$
a^5 + b^5 + c^5 + 8(ab + bc + ca) \ge 27.
$$
MathNet 2019-part-05 — 184 problems (EN–VI) Question 102
Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)