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?
2026-04-01 10:24:42.1775039082
Minimum value of $\frac{(1 + x + x^2)(1 + y + y^2)}{xy}$
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$$\frac{(1+x+x^2)(1+y+y^2)}{xy} = \frac{1+x+x^2}{x} \cdot \frac{1+y+y^2}{y}$$
By AM–GM inequality $(1+x+\frac1x)(1+y+\frac1y)≥3*3=9$