### How to find all rational solutions of $\ x^2 + 3y^2 = 7$?
I knew that for $x^2 + y^2 = 1$ the x and y can be expressed by introducing one more variable where $\ m=y/(x+1)$, then $\ x= 2m/(1+m^2)$ and $\ y= (1-m^2)/(1+m^2)$. What about $\ x^2 + 3y^2 = 7$,...