$$
\begin{aligned}
y=\sqrt{2 x^{2}} & -2 x+1 \\
& +\sqrt{2 x^{2}-(\sqrt{3}-1) x+1} \\
& +\sqrt{2 x^{2}-(\sqrt{3}+1) x+1}
\end{aligned}
$$

Find the minimum value of the function above.
Obviously, since
\[
\begin{aligned}
y=\sqrt{x^{2}}+ & (x-1)^{2} \\
& +\sqrt{\left(x-\frac{\sqrt{3}}{2}\right)^{2}+\left(x+\frac{1}{2}\right)^{2}} \\
+ & \sqrt{\left(x-\frac{\sqrt{3}}{2}\right)^{2}+\left(x-\frac{1}{2}\right)^{2}},
\end{aligned}
\]
then for the points \( T(x, x), A(0,1), B\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right), C\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right) \), we have \( y = TA + TB + TC \). It is easy to verify that \( \triangle ABC \) is an equilateral triangle centered at \( O(0, 0) \) with side length 1. According to the Fermat point principle, when \( T \) coincides with \( O \), \( TA + TB + TC \) reaches its minimum value. Therefore, the minimum value of \( y \) is obtained when \( T(0,0) \), which is \( y(0) = 3 \).