Question

 Giải pt sau:

cos3x+cos2x+cosx+1=0

Answer 1

\(\Leftrightarrow cos3x+cosx+cos2x+1=0\)

\(\Leftrightarrow2cos2x.cosx+2cos^2x-1+1=0\)

\(\Leftrightarrow2cosx\left(cos2x+cosx\right)=0\)

\(\Leftrightarrow2cosx\left(2cos^2x-1+cosx\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\cosx=-1\\cosx=\dfrac{1}{2}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=\pi+k2\pi\\x=\pm\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\) (\(k\in Z\))