If x⁴ + y⁴ + x²y² = 21 and x² + y² - xy = 7, then what is the value of x/y + y/x ?

If x⁴ + y⁴ + x²y² = 21 and x² + y² - xy = 7, then what is…

If x⁴ + y⁴ + x²y² = 21 and x² + y² - xy = 7, then what is the value of $\frac{x}{y}$ + $\frac{y}{x}$ ?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. - $\frac{5}{2}$

⇒ x² + y² - xy = 7

⇒ x² + y² = 7 + xy........(1)

⇒ x⁴ + y⁴ + x²y² = 21

on adding 2x²y² on both sides we get

⇒ (x² + y²)² = 21 + x²y²

⇒ (7 + xy)² = 21 + x²y²

⇒ 49 + x²y² + 14xy = 21 + x²y²

⇒ 14xy = -28

⇒ xy = -2

⇒ x² + y² = 7 - 2 = 5

⇒ $\frac{x}{y}$ + $\frac{y}{x}$ can be written as ( x² + y²)/xy

⇒ -5/2