Question

If $\frac{x+1}{x}=4$, find the value of $\frac{x^4+1}{x^4}$.

Answer 1

$\frac{x+1}{x}=4$

$\frac{x^4+1}{x^4}$

$\frac{x+1}{x}=4$

$\Rightarrow 1+\frac{1}{x}=4$

$\Rightarrow \frac{1}{x}=3$

$\Rightarrow {\left(\frac{1}{x}\right)}^4=3^4$

$\Rightarrow \frac{1}{x^4}=81$

$\frac{x^4+1}{x^4}=1+\frac{1}{x^4}=1+81=82$