Question

if x+1/x=2,find x²+1/x²& x⁴+1/x⁴

Answer 1

Given Equation is x + 1/x = 2

On squaring both sides, we get

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

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

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

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

x^2 + 1/x^2 = 2. 


On Squaring both sides, we get

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

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

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

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

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


Hope this helps!