Question

if x+x^-1 = root 5 evaluate x^2+x^-2 and x^4+x^-4

Answer 1

Answer:

Step-by-step explanation:

X+1/x=√5 (given)

Now,

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

(√5)^2 = x^2 + 1/x^2 + 2

5 = x^2 + 1/x^2 + 2

5-2 = x^2 + 1/x^2

3 = x^2 + 1/x^2

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

(3)^2 = x^4 + 1/x^4 + 2

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

9 - 2 = x^4 + 1/x^4

7 = x^4 + 1/x^4