f: \(\Leftrightarrow\tan x-\dfrac{1}{\tan x}=\dfrac{3}{2}\)
\(\Leftrightarrow\dfrac{tan^2x-1}{tanx}=\dfrac{3}{2}\)
\(\Leftrightarrow2tan^2x-2-3tanx=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=2\\tanx=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=arctan\left(2\right)+k\Pi\\x=arctan\left(-\dfrac{1}{2}\right)+k\Pi\end{matrix}\right.\)
i: \(\Delta=\left(\sqrt{3}-1\right)^2-4\cdot\left(\sqrt{3}\right)=4-2\sqrt{3}+4\sqrt{3}=4+2\sqrt{3}=\left(\sqrt{3}+1\right)^2\)
Pt có hai nghiệm phân biệt là:
\(\left[{}\begin{matrix}tanx=\dfrac{-\sqrt{3}+1-\sqrt{3}-1}{2}=-\sqrt{3}\\tanx=\dfrac{-\sqrt{3}+1+\sqrt{3}+1}{2}=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\Pi+k\Pi\\x=\dfrac{\Pi}{4}+k\Pi\end{matrix}\right.\)