Question

If $x+\frac{1}{x}=2$ then find the value of $x^4+\frac{1}{x^4}$.

Answer 1

Given,

$x+\frac{1}{x}=2$

or, $x^2-2x+1=0$

or, $(x-1{)}^2=0$

or, $x=1,1$.

Now for $x=1$ we've,

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

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

$=1+1$

$=2$.