Question

If x+1/x=5, find the value of x³+1/x³

Answer 1

★Given:-

$\sf x + \dfrac{1}{x} = 5$

★To Find:-

$\sf x^3 + \dfrac{1}{x^3}$

★Solution

We know that,

$\sf (a+b)^3 = a^3+b^3+3ab(a+b)$

Using this identity,

$\sf \Bigg ( x + \dfrac{1}{x} \Bigg )^3$ $\sf = (x)^3 + \Bigg ( \dfrac{1}{x} \Bigg )^3 + 3 \times x \times \dfrac{1}{x}( x + \dfrac{1}{x})$

$\sf \implies (5)^3 = x^3 + \dfrac{1}{x^3} + 3(5)$

$\sf \implies 125 = x^3 + \dfrac{1}{x^3} + 15$

$\sf \implies 125 - 15 = x^3 + \dfrac{1}{x^3}$

$\sf \implies 110 = x^3 + \dfrac{1}{x^3}$

Hope it helps...