Find the square root of the polynomial My question is:
Find the square root of the polynomial-
$$\frac{x^2}{y^2} + \frac{y^2}{x^2} - 2\left(\frac{x}y + \frac{y}x\right) + 3$$

The polynomial is
$ \frac{x^2}{y^2} + \frac{y^2}{x^2} - 2\left( \frac{x}{y} + \frac{y}{x} \right) + 3$
Denote $ z = \frac{x}{y}$ and have
$ z^2 + z^{-2} - 2(z+z^{-1}) + 3 $
Assume $y \ne 0$ and multiply by $z^2$ and have
$ z^4 + 1 - 2z^3 - 2z + 3z^2 = 0$
Instructions how to solve a general quartic equation can be found in Wikipedia. 
