<s>[INST] Find the square root of the polynomial My question is:
Find the square root of the polynomial-
$$\frac{x^2}{y^2} + \frac{y^2}{x^2} - 2\left(\frac{x}y + \frac{y}x\right) + 3$$
 [/INST] $$\frac{x^2}{y^2} + \frac{y^2}{x^2} - 2\left(\frac{x}y + \frac{y}x\right) + 3$$
$$=\frac{{x^4} + {y^4} - 2\left({x^2} +{y^2}\right)xy + 3{x^2}{y^2}}{{x^2}{y^2}}$$  $$=\frac{{x^4} + {y^4} + 2{x^2}{y^2}+ {x^2}{y^2} - 2\left({x^2} +{y^2}\right)xy }{{x^2}{y^2}}$$  $$=\frac{({x^2}+{y^2})^2+ {(xy)^2} - 2\left({x^2} +{y^2}\right)xy }{{x^2}{y^2}}$$  $$=\frac{({x^2}+{y^2} - xy)^2}{{(xy)^2}}$$
the square root of the polynomial =  $$\pm \frac{{x^2}+{y^2} - xy}{xy}$$ 
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