if-x-y-z-gt-0-such-that-x-y-z-3-and-0-then-prove-that-x-y-3-y-2-y-z-3-z-2-z-x-3-x-2-3-1-

Question Number 161433 by HongKing last updated on 17/Dec/21

if x; y; z > 0 such that x + y + z = 3

and λ ⩾ 0 then prove that :

\frac{x}{y^{3} + λ y^{2}} + \frac{y}{z^{3} + λ z^{2}} + \frac{z}{x^{3} + λ x^{2}} ⩾ \frac{3}{λ + 1}