Question

if [x+1/x] =5 find the value of (x^2 +1/x^2) and (x^4 +1/x^4​

Answer 1

Answer:

(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

Step-by-step explanation:

x+1/x = 5

(x+1/x)² = x²+1/x²+2

(5)² = x²+1/x²+2

25-2 = x²+1/x² => 23

(x²+1/x²)² = x⁴+1/x⁴+2

(23)² = x⁴+1/x⁴+2

529-2 = x⁴+1/x⁴

527 = x⁴+1/x⁴

hope this helps