Question 9
Find all positive real numbers $x$ and $y$ such that
$$
x^{x+y} = y^{x-y} \quad \text{and} \quad x^2y = 1
$$
$$
x^{x+y} = y^{x-y} \quad \text{and} \quad x^2y = 1
$$
MathNet 2008-part-04 — 165 problems (EN–VI) Question 9
Math Olympiad Vault · MathNet 2008-part-04 — 165 problems (EN–VI)