# Prove that if x≠0 then if y= 3x^2+2y/x^2+2 then y=3

bean29
suppose that x and y are real numbers. Prove that if x≠0 then if y= 3x^2+2y/x^2+2 then y=3

y(1-2/x2) = 3x2 + 2

y = (3x4 + 2x2)/(x2-2)

Doesn't look constant.

$$y = \frac{3x^2+2y}{x^2+2}$$.
$$y x^2 + 2y = 3x^2 + 2y \Leftrightarrow y x^2 = 3 x^2 \Leftrightarrow y = 3$$