Question

Find all the Real Solutions for the following equations.

\[x^3 - 3x = y\]
\[y^3 - 3y=z\]
\[z^3 - 3z = x\]

Answer 1

(z^2 - 3) (x^2 - 3) (y^2 - 3) = 1

Answer 2

x (x^2 - 3) = y

x^2 - 3 = y/x

y (y^2 - 3) = z

y^2 - 3 = z/y

z (z^2 - 3) = x

z^2 - 3 = x/z

(z^2 - 3) (x^2 - 3) = y/z

(z^2 - 3) (x^2 - 3) = 1/ (y^2 - 3)

(z^2 - 3) (x^2 - 3) (y^2 - 3) = 1