Toán Lớp 11: Phương trình (2m-3)cos²2x=4(m-1) có nghiệm khi ?
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Toán Lớp 11: Phương trình (2m-3)cos²2x=4(m-1) có nghiệm khi ?
Comments ( 2 )
0.{\cos ^2}2x = 4.\left( {\dfrac{3}{2} – 1} \right)\\
\Leftrightarrow 0 = 2
\end{array}\)
\left( {2m – 3} \right).{\cos ^2}2x = 4.\left( {m – 1} \right)\\
\Leftrightarrow {\cos ^2}2x = \dfrac{{4.\left( {m – 1} \right)}}{{2m – 3}}\\
– 1 \le \cos 2x \le 1 \Rightarrow 0 \le {\cos ^2}2x \le 1
\end{array}\)
0 \le \dfrac{{4.\left( {m – 1} \right)}}{{2m – 3}} \le 1\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{{4\left( {m – 1} \right)}}{{2m – 3}} \ge 0\\
\dfrac{{4.\left( {m – 1} \right)}}{{2m – 3}} \le 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\dfrac{{m – 1}}{{2m – 3}} \ge 0\\
\dfrac{{4m – 4}}{{2m – 3}} – 1 \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
m > \dfrac{3}{2}\\
m \le 1
\end{array} \right.\\
\dfrac{{2m – 1}}{{2m – 3}} \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
m > \dfrac{3}{2}\\
m \le 1
\end{array} \right.\\
\dfrac{1}{2} \le m < \dfrac{3}{2}
\end{array} \right. \Leftrightarrow \dfrac{1}{2} \le m \le 1
\end{array}\)