Question 163
Prove that if $x, y, z$ are positive real numbers, then
$$
x^{2}+2 y^{2}+3 z^{2} \gt x y+3 y z+z x .
$$
$$
x^{2}+2 y^{2}+3 z^{2} \gt x y+3 y z+z x .
$$
MathNet 2019-part-07 — 184 problems (EN–VI) Question 163
Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)