Had this equation come up in class, I know the answer is $$y=\frac{x - \sqrt{x^{2} + 8}}{2}$$ $$y=\frac{x +\sqrt{x^{2} + 8}}{2}$$
but I am not sure how they got there from. $$x = y - 2/y$$/
I'm just curious so if anybody could help explain it would be greatly appreciated.
If you multiply the equation through by $y$ you get
$$xy = y^2 -2$$
Move everything to one side and you get
$$y^2 - xy -2 = 0$$
Treating $x$ as a constant, this is just a quadratic equation in $y$, so we can apply the quadratic formula to it. The "$b$" that goes in the quadratic formula depends on $x$ but that doesn't matter, we can just plug it in anyway.