If x2 + 1/x2 = 79, find the value of x + 1/x
Question:

If $x^{2}+1 / x^{2}=79$, find the value of $x+1 / x$

Solution:

We have,

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

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

$\Rightarrow(x+1 / x)^{2}=79+2 \quad\left[\therefore x^{2}+1 / x^{2}=79\right]$

$\Rightarrow(x+1 / x)^{2}=81$

$\Rightarrow(x+1 / x)^{2}=(\pm 9)^{2}$

$\Rightarrow x+1 / x=\pm 9$