本帖最后由 isee 于 2022-3-4 23:27 编辑
常规计算如下。
设$ED=x$,则
\begin{align*}
\vv {EA}\cdot\vv{EB}&=(\vv{ED}+\vv{DA})(\vv{EC}+\vv{CB})\\
&=\vv{ED}\cdot\vv{EC}+\vv{ED}\cdot\vv{CB}+\vv{DA}\cdot\vv{EC}+\vv{DA}\cdot\vv{CB}\\
&=-x(\sqrt 3-x)+\frac {\sqrt 3 x}2+0+\frac{3}2\\
&=\left(x-\frac {\sqrt 3}4\right)^2+\frac{21}{16}\\
&\geqslant \frac {21}{16}
\end{align*} |