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

 

[mathman]

y(1-2/x²) = 3x² + 2

y = (3x⁴ + 2x²)/(x²-2)

Doesn't look constant.

 

[rubi]

It looks like he wanted to write
$$y = \frac{3x^2+2y}{x^2+2}$$.
Then it works out:
$$y x^2 + 2y = 3x^2 + 2y \Leftrightarrow y x^2 = 3 x^2 \Leftrightarrow y = 3$$

 

[mfb]

This is not an acceptable way to ask for help at homework problems. In addition, it is in the wrong forum.