Question

If $x^4+\frac{1}{x^4}=194,$find $x^3+\frac{1}{x^3},x^2+\frac{1}{x^2}$and $x+\frac{1}{x}$

Answer 1

In the given problem, we have to find the value of

Given

By adding and subtracting in left hand side of we get,

Again by adding and subtracting in left hand side of we get,

Now cubing on both sides of we get

we shall use identity

Hence the value of is respectively.