Toán cos2x +3cosx+ 2=0 có tất cả m nghiệm. tìm nghiệm 14/07/2021 By Nevaeh cos2x +3cosx+ 2=0 có tất cả m nghiệm. tìm nghiệm
$\text{cos2x}+3\text{cosx}+2=0$ $↔ 2\text{cosx}^2x+3\text{cosx}+1=0$ $↔ \left[ \begin{array}{l}\text{cosx}=-1\\\text{cosx}=-\dfrac{1}{2}\end{array} \right.$ $↔ \left[ \begin{array}{l}x=\pi+k2\pi\\x=±\dfrac{2\pi}{3}+k2\pi\end{array} \right.$ ($k∈\mathbb{Z}$) Trả lời
$\cos2x+3\cos x+2=0$ $\Leftrightarrow 2\cos^2x+3\cos x-1+2=0$ $\Leftrightarrow 2\cos^2x+3\cos x +1=0$ $\Leftrightarrow \cos x=-0,5$ hoặc $\cos x=-1$ $+) \cos x=-0,5\Leftrightarrow x=\pm\dfrac{2\pi}{3}+k2\pi$ $+) \cos x=-1\Leftrightarrow x=\pi+k2\pi$ Trả lời
$\text{cos2x}+3\text{cosx}+2=0$
$↔ 2\text{cosx}^2x+3\text{cosx}+1=0$
$↔ \left[ \begin{array}{l}\text{cosx}=-1\\\text{cosx}=-\dfrac{1}{2}\end{array} \right.$
$↔ \left[ \begin{array}{l}x=\pi+k2\pi\\x=±\dfrac{2\pi}{3}+k2\pi\end{array} \right.$ ($k∈\mathbb{Z}$)
$\cos2x+3\cos x+2=0$
$\Leftrightarrow 2\cos^2x+3\cos x-1+2=0$
$\Leftrightarrow 2\cos^2x+3\cos x +1=0$
$\Leftrightarrow \cos x=-0,5$ hoặc $\cos x=-1$
$+) \cos x=-0,5\Leftrightarrow x=\pm\dfrac{2\pi}{3}+k2\pi$
$+) \cos x=-1\Leftrightarrow x=\pi+k2\pi$