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MathNet 2003 — Part 02 Question 80

Math Olympiad Vault · MathNet 2003 — Part 02

Question 80

The real numbers $x$ and $y$ satisfy the equalities
$$
\sqrt{3x}\left(1+\frac{1}{x+y}\right)=2, \quad \sqrt{7y}\left(1-\frac{1}{x+y}\right)=4\sqrt{2}
$$
Find the numerical value of the ratio $y / x$.