Why is my solution incorrect? AM GM inequality – math.stackexchange.com

The problem is: Let $p+2q=3$ and find the maximum of $pq$. Of course I could solve this as below: $$pq=(3-2q)q=-2(q-\frac{3}{4})^2+\frac{9}{8}$$ so, the maximum is $\frac{9}{8}$. However, I got ...

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