Question

Tìm nghiệm của pt: \(tan^2x+5tanx-6=0\) trên tập \(\left[0;2\pi\right]\)

Answer 1

\(tan^2x+5tanx-6=0\Rightarrow\left[{}\begin{matrix}tanx=1\\tanx=-6\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+k\pi\\x=arctan\left(-6\right)+l\pi\end{matrix}\right.\)

\(0\le x\le2\pi\) \(\Rightarrow\left\{{}\begin{matrix}0\le\frac{\pi}{4}+k\pi\le2\pi\\0\le arctan\left(-6\right)+l\pi\le2\pi\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}k=\left\{0;1\right\}\\l=\left\{1;2\right\}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}\\x=\frac{5\pi}{4}\\x=arctan\left(-6\right)+\pi\\x=arctan\left(-6\right)+2\pi\end{matrix}\right.\)