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MathNet 2019-part-07 — 184 problems (EN–VI) Question 84

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 84

It is known that nonzero real numbers $x$, $y$, $z$ satisfy the condition $xy + yz + zx = 0$. What value can the expression
$$
\frac{1}{x^2+2yz} + \frac{1}{y^2+2zx} + \frac{1}{z^2+2xy}
$$
be equal to?