Simultaneous equations

3x^2 = 2tx
-z = 2ty
-y = 2tz
x^2 + y^2 + z^2 = 2

Solve for x,y,z (if possible!?)

>>8

Oopsie, the last two should be


(-1/3, √(17/18), √(17/18))
(-1/3, -√(17/18), -√(17/18))

If the bottom sign is chosen, y=z