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Question:
If $(x+1 / x)=5$, Find the value of $x^{3}+1 / x^{3}$
Solution:
Given, $(x+1 / x)=5$
We know that, $(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b)$ ... 1
Substitute (x + 1/x) = 5 in eq1
$(x+1 / x)^{3}=x^{3}+1 / x^{3}+3\left(x^{*} 1 / x\right)(x+1 / x)$
$5^{3}=x^{3}+1 / x^{3}+3(x * 1 / x)(x+1 / x)$
$125=x^{3}+1 / x^{3}+3(x+1 / x)$
$125=x^{3}+1 / x^{3}+3(5)$
$125=x^{3}+1 / x^{3}+15$
$125-15=x^{3}+1 / x^{3}$
$x^{3}+1 / x^{3}=110$
Hence, the result is $x^{3}+1 / x^{3}=110$