回復 1# P78961118 的帖子
\(\begin{align}
& \overline{AD}=x,\overline{AC}=\sqrt{3},\overline{CD}=\frac{\sqrt{3}}{2} \\
& \cos \angle DAC=\frac{{{x}^{2}}+3-\frac{3}{4}}{2\sqrt{3}x}=\frac{x}{2\sqrt{3}}+\frac{9}{8\sqrt{3}x}\ge 2\sqrt{\frac{x}{2\sqrt{3}}\times \frac{9}{8\sqrt{3}x}}=\frac{\sqrt{3}}{2} \\
& \angle DAC\le {{30}^{{}^\circ }} \\
\end{align}\)
等號成立於\(x=\frac{3}{2}\)
