If (x + 1/x) = 5, Find the value of x3 + 1/x3

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 $x^{3}+1 / x^{3}=110$

 

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