Tổng nghiệm trong đoạn 0;3pi của phương trình 1-2cos bình phương 2 x - sin x = 0 là j ạ
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$1-2{\cos}^22x-\sin x=0$ $\Rightarrow-(\cos 4x)-\sin x=0$ $\Rightarrow\cos 4x=-\sin x=\sin(-x)=\cos(\dfrac{\pi}{2}+x)$ $\Rightarrow 4x=\pm(\dfrac{\pi}{2}+x)+k2\pi$ $\Rightarrow \left[ \begin{array}{l} x=\dfrac{\pi}{6}+k\dfrac{2\pi}{3} \\ x=\dfrac{-\pi}{10}+k\dfrac{2\pi}{5}\end{array} \right .$ +) $0\le\dfrac{\pi}{6}+k\dfrac{2\pi}{3} \le3\pi$ $\Rightarrow \dfrac{-1}{4}\le k\le\dfrac{17}{4}$ $\Rightarrow k=\{0;1;2;3;4\}$ $\Rightarrow x=\{\dfrac{\pi}{6};\dfrac{5\pi}{6};\dfrac{3\pi}{2};..\dfrac{17\pi}{6}\}$ +) $0\le\dfrac{-\pi}{10}+k\dfrac{2\pi}{5} \le3\pi$ $\Rightarrow 0,25\le k\le7,75$ $\Rightarrow k=\{1;2;3;4;5;6;7\}$ $\Rightarrow x=\{\dfrac{3\pi}{10};\dfrac{7\pi}{10};..\dfrac{27\pi}{10}\}$ $\Rightarrow \sum=18\pi$
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