Question

If (x+1/x)=5 find the value of (x⁴+1/x⁴)​

Answer 1

$x+\frac{1}{x} =5$ is given, solve $x^4+\frac{1}{x^4}$.

Identity!

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

Thus, $x^2+\frac{1}{x^2}=(x+\frac{1}{x} )^2-2$.

On the other hand, $(x^4+\frac{1}{x^4} )=(x^2+\frac{1}{x^2} )^2-2$.

$x^2+\frac{1}{x^2}=23$

∴$x^4+\frac{1}{x^4} =527$

I elided complicated calculation such as 23²-2.