Question

If (x+1/x)^2 = 3 show that (x^3+1/x^3)=0

Answer 1

(x+1/x)^2 = 3 
x+1/x=root3
cubing on both sides
x^3+1/x^3+3(x+1/x)=3 root 3
x^3+1/x^3+3root 3=3 root 3
x^3+1/x^3 = 0

Answer 2

Answer:

Proved (x^3+1/x^3) = 0

Step-by-step explanation:

(x+1/x) ^2 = 3  

x + 1/x = √3

Take a cube both side,

x^3 + 1/x^3 + 3 (x + 1/x) = (√3 )³

x^3 + 1/x^3 + 3 √3 = (√3 )³

x^3+1/x^3 = 3 √3 - 3√3  = 0

(x+1/x)^2 = 3  

x + 1/x = √3

Hence proved (x^3+1/x^3) = 0