Question

If x2 - 4x + 1 = 0, find the value of x4 + 1/x4​

Answer 1

x^2 - 4x + 1 = 0

divide it by x

x- 4+ 1/x =0

or

x + 1/x =4

Now square it

(x + 1/x)^2 =4^2

=>

x^2 + 1/x^2 + 2 = 16

=>

x^2 + 1/x^2 = 14

Again square it

(x^2 + 1/x^2)^2 =14^2

=>

x^4 + 1/x^4 + 2 = 196

=>

x^4 + 1/x^4 = 194