Question

if {x + (1/x)} =√5,find the values of {x^2 + (1/x^2)} and {x^4 + (1/x^4)}.

Answer 1

So the given equation is, x+1/x=2.

Thus, 2x=x+1.

Hence, x=1.

I hope we are clear till here.

The question asked is x^4 - 1/x^4.

Putting the value of x that we obtained from the given equation(i.e. x=1) in the second equation we get,

1^4 - 1/1^4 = 1 -1/1 = 1-1 = 0.