<s>[INST] Minimum value of $\frac{(1 + x + x^2)(1 + y + y^2)}{xy}$ 
What is the minimum value of $$\frac{(1 + x + x^2)(1 + y + y^2)}{xy},~~(x \neq 0)$$

Should we find the minimum value of each quadratic? 
 [/INST] $$\frac{(1+x+x^2)(1+y+y^2)}{xy} = \frac{1+x+x^2}{x} \cdot \frac{1+y+y^2}{y}$$
By AM–GM inequality $(1+x+\frac1x)(1+y+\frac1y)≥3*3=9$
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