Question

Giải pt ( đưa về pt bậc 2 )

1. tan²x - 5tanx + 6 = 0

2. 3cos²2x + 4cos2x + 1 = 0

Answer 1

1.

\(tan^2x-5tanx+6=0\)

\(\Rightarrow\left[{}\begin{matrix}tanx=2\\tanx=3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=arctan\left(2\right)+k\pi\\x=arctan\left(3\right)+k\pi\end{matrix}\right.\)

2.

\(3cos^22x+4cos2x+1=0\)

\(\Rightarrow\left[{}\begin{matrix}cos2x=-1\\cos2x=-\dfrac{1}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=\pi+k2\pi\\2x=\pm arccos\left(-\dfrac{1}{3}\right)+k2\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=\pm\dfrac{1}{2}arccos\left(-\dfrac{1}{3}\right)+k\pi\end{matrix}\right.\)