If (x²)/(y²)+(y²)/(x²)=7 , What is the value of (x³)/(y³)+(y³)/(x³) is:

If (x²)/(y²)+(y²)/(x²)=7 , What is the value of…

If $\dfrac{x^2}{y^2}+\dfrac{y^2}{x^2}=7$ , What is the value of $\dfrac{x^3}{y^3}+\dfrac{y^3}{x^3}$ is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 18.

Let's assume x/y = a

a² + 1/a² = 7

⇒ a² + 1/a² + 2 = 9

⇒ (a + 1/a)² = 9 ⇒ (a + 1/a) = 3

Cubing both the sides, a³ + 1/a³ + 3(a + 1/a) = 27

⇒ a³ + 1/a³ + 3 × 3 = 27

⇒ a³ + 1/a³ = 27 - 9 = 18

⇒ $\frac{x^3}{y^3}+\frac{y^3}{x^3} = 18$