Question

А)cos4x-cosx=0 решить Б) найти все корни, принадлежащие [3π;7π/2]

Answer 1

$cos4x-cosx=0\Leftrightarrow cos4x=cosx\\\left[ \begin{gathered} 4x=x+2\pi k \\ 4x=-x+2\pi k \\ \end{gathered} \right.\Rightarrow x=\left \{ \frac{2\pi k}{3}; \frac{2\pi k}{5}\right \},k\in \mathbb{Z}\\\left [ 3\pi;\frac{7\pi}{2} \right ]\Rightarrow k=\left \{5;8 \right \}\Rightarrow x=\left \{ \frac{16\pi}{5}; \frac{10\pi}{3}\right \}$