Question 112
Given real numbers $x, y, z$, with
$$
x + y + z = xy + yz + zx = -1.
$$
Prove that $(xy - z^2)(yz - x^2)(zx - y^2) = xyz - 1$.
$$
x + y + z = xy + yz + zx = -1.
$$
Prove that $(xy - z^2)(yz - x^2)(zx - y^2) = xyz - 1$.
MathNet 2016-part-01 — 184 problems (EN–VI) Question 112
Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)