Question:
If $(x-1 / x)=5$, Find the value of $x^{3}-1 / x^{3}$
Solution:
Given, If $(x-1 / x)=5$
We know that, $(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b) \ldots 1$
Substitute $(x-1 / x)=5$ in eq 1
$(x-1 / x)^{3}=x^{3}-1 / x^{3}-3\left(x^{*} 1 / x\right)(x-1 / x)$
$5^{3}=x^{3}-1 / x^{3}-3(x-1 / x)$
$125=x^{3}-1 / x^{3}-\left(3^{*} 5\right)$
$125=x^{3}-1 / x^{3}-15$
$125+15=x^{3}-1 / x^{3}$
$x^{3}-1 / x^{3}=140$
Hence, the result is $x^{3}-1 / x^{3}=140$