Question

If (x-2/x) = 6, find the value of (x^3 - 8/x^3)​

Answer 1

Answer:

The value of $x^{3}-\frac{8}{x}^{3}$ is 252.

Step-by-step explanation:

The formula of (a - b)³ is:

$(a-b)^{3}=a^{3}-b^{3}-3ab(a-b)$

Use this relation to solve the provided problem as follows:

$(x-\frac{2}{x})^{3}=x^{3}-(\frac{2}{x})^{3}-3.x.\frac{2}{x}(x-\frac{2}{x})\\6^{3}=x^{3}-\frac{8}{x}^{3}-36\\216+36=x^{3}-\frac{8}{x}^{3}\\x^{3}-\frac{8}{x}^{3}=252$

Thus, the value of $x^{3}-\frac{8}{x}^{3}$ is 252.