Question

If x-1/x = 3 , Find the value of x³-1/x³​

Answer 1

Required Answer:-

Given:

• x - 1/x = 3

To Find:

• Value of x³ - 1/x³

Solution:

We have,

$\rm \implies x - \dfrac{1}{x} = 3$

Cubing both sides, we get,

$\rm \implies \bigg(x - \dfrac{1}{x} \bigg)^{3} = {3}^{3}$

$\rm \implies {x}^{3} - \dfrac{1}{ {x}^{3} } - 3 \times x \times \dfrac{1}{x} \bigg(x - \dfrac{1}{x} \bigg) = {3}^{3}$

$\rm \implies {x}^{3} - \dfrac{1}{ {x}^{3} } - 3\bigg(x - \dfrac{1}{x} \bigg) = {3}^{3}$

$\rm \implies {x}^{3} - \dfrac{1}{ {x}^{3} } - 9 =27$

$\rm \implies {x}^{3} - \dfrac{1}{ {x}^{3} } =27 + 9$

$\rm \implies {x}^{3} - \dfrac{1}{ {x}^{3} } = 36$

★ Therefore, the value of x³ - 1/x³ is 36.

Answer:

• x³ - 1/x³ = 36

Identity Used:

• (a - b)³ = a³ - b³ - 3ab(a - b)