\(\begin{array}{l}
2\cos 2x + 2\cos x - \sqrt 2 = 0\\
\Leftrightarrow 2\left( {2{{\cos }^2}x - 1} \right) + 2\cos x - \sqrt 2 = 0\\
\Leftrightarrow 4{\cos ^2}x + 2\cos x - 2 - \sqrt 2 = 0\\
\Leftrightarrow \cos x = \frac{{\sqrt 2 }}{2}\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{4} + k2\pi \Rightarrow x \in \left\{ {\frac{\pi }{4};\frac{{9\pi }}{4};...;\,\frac{{8065\pi }}{4}} \right\}\\
x = \frac{{ - \pi }}{4} + k2\pi \Rightarrow x \in \left\{ {\frac{{7\pi }}{4};\frac{{15\pi }}{4};...;\,\frac{{8063\pi }}{4}} \right\}
\end{array} \right.
\end{array}\)
\( \Rightarrow \) Có \(2017\)nghiệm.
