NZ-NZMO 2021 Problem 2

Prove that

$x^{2} + \frac{8}{xy} +y^{2}\geq 8.$

for all positive real numbers $x$ and $y$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

x^{2} + \frac{8}{x y} + y^{2}\geq 8

Solutions

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