Question

\(\left(\sqrt{3}+1\right)x^3-\sqrt{3}x^2-x=0\)

Answer 1

\(\Leftrightarrow x\cdot\left[\left(\sqrt{3}+1\right)x^2-\sqrt{3}x-1\right]=0\Leftrightarrow x\cdot\left[\left(\sqrt{3}+1\right)x^2-\left(\sqrt{3}+1\right)x+x-1\right]=0\Leftrightarrow x\cdot\left(x-1\right)\left[\left(\sqrt{3}+1\right)x+1\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=\dfrac{-1}{\sqrt{3}+1}=-\dfrac{\left(\sqrt{3}-1\right)}{3-1}=\dfrac{-\sqrt{3}+1}{2}\end{matrix}\right.\)