Cho phương trình \(cos3x –...

B

- Hướng dẫn giải

Ta có: \(\cos 3x - 4\cos 2x + 3\cos x - 4 = 0\)

\(\Leftrightarrow 4{\cos ^3}x - 3\cos x - 4\left( {2{{\cos }^2}x - 1} \right) + 3\cos x - 4 = 0\)

\(\Leftrightarrow 4{\cos ^3}x - 8{\cos ^2}x = 0 \Leftrightarrow 4{\cos ^2}x\left( {{{\cos }}x - 2} \right) = 0\)

\(\Leftrightarrow \left[ \begin{array}{l}\cos x = 0\\\cos x = 2\end{array} \right. \) \(\Leftrightarrow x = \dfrac{\pi }{2} + k\pi \;\left( {k \in \mathbb{Z}} \right)\)

Với

\(x = \dfrac{\pi }{2} + k\pi \in \left[ {0;14} \right] \) \(\Rightarrow k \in \left[ { - \dfrac{1}{2};3,956} \right] \) \(\Rightarrow k \in \left\{ {0;1;2;3} \right\}\)