Question

if (x+1÷x)^2=4 find value of x^4+1÷x^4

Answer 1

(x+1/x)^2=4
x^2+1/x^2+2=4
x^2+1/x^2=2
squaring on both sides
(x^2+1/x^2)^2=4
x^4+1/x^4+2=4
x^4+1/x^4=2