Question

Q.2)If x-2/x=3 then X³-8/x³ is equal to

27

36

45

54​

Answer 1

Given

$\sf x - \dfrac{2}{x} = 3$

To find

$\sf x^3 - \dfrac{8}{x^3}$

Solution

Cubing $\sf x - \dfrac{2}{x}$ will give,

$\sf \Bigg ( x- \dfrac{2}{x} \Bigg )^3$

Using the identity (a-b)³ = a³-b³-3ab(a-b)

$\sf \implies \Bigg ( x- \dfrac{2}{x} \Bigg )^3 = (x)^3 - \Bigg ( \dfrac{2}{x} \Bigg )^3 - 3 \times x \times \dfrac{2}{x} \Bigg ( x - \dfrac{2}{x} \Bigg )$

$\sf \implies (3)^3 = x^3 - \dfrac{8}{x^3} - 3 \times 2(3)$

$\sf \implies 27 = x^3 - \dfrac{8}{x^3} - 3\times 6$

$\sf \implies 27 = x^3 - \dfrac{8}{x^3} - 18$

$\sf \implies 27+18 = x^3 - \dfrac{8}{x^3}$

$\sf \implies 45= x^3 - \dfrac{8}{x^3}$

$\boxed{ \bold{ x^3 - \dfrac{8}{x^3} = 45}}$

Hence, 45 is the correct answer!