Question

if x-1/x=√5 find the value of x^2+1/x^2 and x^4+1/x^4❤❤


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Answer 1

Answer:

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