Question

If x^4 +1/x^4 = 2 , Find the value of
(i) x^2 + 1/x^2
(ii) x+1/x
(iii) x^3 + 1/x^3

Answer 1

Step-by-step explanation:

1. x⁴+1/x⁴=2

Adding 2 on both sides

→x⁴+1/x⁴+2=4

→(x²+1/x²)²=4

→x²+1/x²=√4=2

2. x²+1/x²=2

Adding 2 on both sides

→x²+1/x²+2=4

→(x+1/x)²=4

→x+1/x=√4=2

3. x+1/x=2

Cubing on both sides

→(x+1/x)³=8

→x³+1/x³+3(x+1/x)=8

→x³+1/x³+3(2)=8

→x³+1/x³=8-6=2