Question

If (x- 2/x) = 6, find the value of ( x³ - 8/x³)​

Answer 1

EXPLANATION.

⇒ (x - 2/x) = 6.

As we know that,

Cubing on both sides of the equation, we get.

⇒ (x - 2/x)³ = (6)³.

⇒ (x)³ - 3(x)²(2/x) + 3(x)(2/x)² - (2/x)³ = (6)³.

⇒ x³ - (6x) + (12/x) - (8/x³) = 216.

⇒ x³ - 6(x - 2/x) - 8/x³ = 216.

Put the value of (x - 2/x) = 6 in the equation, we get.

⇒ x³ - 6(6) - 8/x³ = 216.

⇒ x³ - 36 - 8/x³ = 216.

⇒ x³ - 8/x³ = 216 + 36.

⇒ x³ - 8/x³ = 252.