Question

2cos²x+cos5x=3

Answer 1

Do \(cosa\le1\) \(\forall a\)

\(\Rightarrow\left\{{}\begin{matrix}2cos^2x\le2\\cos5x\le1\end{matrix}\right.\)

\(\Rightarrow2cos^2x+cos5x\le3\) \(\forall x\)

Dấu "=" xảy ra khi và chỉ khi:

\(\left\{{}\begin{matrix}cos^2x=1\\cos5x=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}sinx=0\\cos5x=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=k\pi\\5x=k2\pi\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=k\pi\\x=\frac{k2\pi}{5}\end{matrix}\right.\) \(\Rightarrow x=k2\pi\)