MT【351】行列式面积公式

(中科大2019)已知平面坐标系上三点$A(1,0),B(0,1),C(x,\dfrac{1}{\sqrt{x}})$求$\Delta ABC$面积的最小值___

分析:$S_{\Delta ABC}=\dfrac{1}{2}
\left|\begin{array}{cccc}
1 & 0 & 1 \\
0 & 1 & 1\\
x & \dfrac{1}{\sqrt{x}} & 1
\end{array}\right|
=\dfrac{1}{2}(x+\dfrac{1}{\sqrt{x}}-1)\ge\dfrac{1}{2}(3*4^{-\frac{1}{3}}-1) $