Toán Lớp 11: Cos2x-3cosx+1=0
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Toán Lớp 11: Cos2x-3cosx+1=0
Giúp em với ạ!
Comments ( 1 )
\cos 2x = 2{\cos ^2}x – 1\\
\cos 2x – 3\cos x + 1 = 0\\
\Leftrightarrow \left( {2{{\cos }^2}x – 1} \right) – 3\cos x + 1 = 0\\
\Leftrightarrow 2{\cos ^2}x – 3\cos x = 0\\
\Leftrightarrow \cos x\left( {2\cos x – 3} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
2\cos x – 3 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\cos x = 0\\
\cos x = \dfrac{3}{2}
\end{array} \right.\\
– 1 \le \cos x \le 1 \Rightarrow \cos x = 0 \Leftrightarrow x = \dfrac{\pi }{2} + k\pi \,\,\,\left( {k \in Z} \right)
\end{array}\)