[tex]|x|\leq\sqrt3\Leftrightarrow -\sqrt3\leq x\leq\sqrt3\\
x\leq\sqrt3\Rightarrow x-\sqrt3\leq0\Rightarrow|x-\sqrt3|=\sqrt3-x\\
\text{si}\\
-\sqrt3\leq x\Rightarrow x+\sqrt3\geq0\Rightarrow|x+\sqrt3|=x+\sqrt3 \\
|x-\sqrt3|+|x-\sqrt3|=\sqrt3-x+x+\sqrt3=2\sqrt3=ct,\ \forall x\in\mathbb{R},|x|\leq\sqrt3 [/tex]
