If (x2 + 1/x2) = 98, Find the value of

Given, $\left(x^{2}+1 / x^{2}\right)=98$

We know that, $(x+y)^{2}=x^{2}+y^{2}+2 x y \ldots 1$

Substitute $\left(x^{2}+1 / x^{2}\right)=98$ in eq 1

$(x+1 / x)^{2}=x^{2}+1 / x^{2}+2 * x^{*} 1 / x$

$(x+1 / x)^{2}=x^{2}+1 / x^{2}+2$

$(x+1 / x)^{2}=98+2$

$(x+1 / x)^{2}=100$

$(x+1 / x)=\sqrt{100}$

$(x+1 / x)=\pm 10$

We need to find $x^{3}+1 / x^{3}$

So, $a^{3}+b^{3}=(a+b)\left(a^{2}+b^{2}-a b\right)$

$x^{3}+1 / x^{3}=(x+1 / x)\left(x^{2}+1 / x^{2}-\left(x^{*} 1 / x\right)\right.$

We know that,

$(x+1 / x)=10$ and $\left(x^{2}+1 / x^{2}\right)=98$

$x^{3}+1 / x^{3}=10(98-1)$

$x^{3}+1 / x^{3}=10(97)$

$x^{3}+1 / x^{3}=970$

Hence, the value of $x^{3}+1 / x^{3}=970$