Question

if x+1/x = root 5 find x2 +1/x2 and x4+1/x4

Answer 1

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

Answer 2

Answer:

x²+1/x²=3 and x^4+1/x^4=7

Step-by-step explanation:

x+1/x = √5

squaring both sides

(x+1/x)² = (√5)²

x²+1/x²+2x*1/x=5

x²+1/x²+2=5

x²+1/x²=5-2=3

x²+1/x²=3-------------------------(1)

squaring both sides

(x²+1/x²)²=3²

x^4+1/x^4+2x² *1/x²=9

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

x^4+1/x^4=9-2=7

Hence x^4+1/x^4=7-------------(2)