Can You Prove Gy^3+(y-G)^3 Equals Zero Given x^2+x+G=0?

[thereddevils]

Homework Statement

If x^2+x+G=0 and y=x+1/x , prove that Gy^3+(y-G)^3=0

Homework Equations

The Attempt at a Solution

Gy^3=x^5+3x^3+3x+1/x+x^4+3x^2+3+1/x^2

(y-G)^3=1/x^3+6/x+3+12x+12x^2+12x^4+6x^5+x^6

They are not equal.

Is this the correct way of doing ?

 

[eumyang]

Does
$$y = x + \frac{1}{x}$$
OR
$$y = \frac{x + 1}{x}$$
?


69

 

[thereddevils]

Does
$$y = x + \frac{1}{x}$$
OR
$$y = \frac{x + 1}{x}$$
?


69

$$y=x+\frac{1}{x}$$