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MathNet 2020 — Math Olympiad Vault — Part 05 Question 31

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 31

If $6xy-\sqrt3x^2=\sqrt3y^2$, calculate
$$
\left(\frac{x}{y}\right)^{4} + \left(\frac{y}{x}\right)^{4}
$$