Question

Giải phương trình sau:

\(2sin\left(2x-\dfrac{\pi}{4}\right)+\sqrt{3}=0\)

Answer 1

Pt \(\Leftrightarrow sin\left(2x-\dfrac{\pi}{4}\right)=-\dfrac{\sqrt{3}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\pi}{4}=-\dfrac{\pi}{3}+k2\pi\\2x-\dfrac{\pi}{4}=\dfrac{4\pi}{3}+k2\pi\end{matrix}\right.\),\(k\in Z\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{24}+k\pi\\x=\dfrac{19\pi}{24}+k\pi\end{matrix}\right.\)\(\left(k\in Z\right)\)

Vậy...
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Answer 2

\(2sin\left(2x-\dfrac{\pi}{4}\right)+\sqrt{3}=0\)

\(\Leftrightarrow sin\left(2x-\dfrac{\pi}{4}\right)=-\dfrac{\sqrt{3}}{2}\)

\(\Leftrightarrow sin\left(2x-\dfrac{\pi}{4}\right)=sin\left(-\dfrac{\pi}{3}\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\pi}{4}=-\dfrac{\pi}{3}+k2\pi\\2x-\dfrac{\pi}{4}=\pi+\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{\pi}{12}+k2\pi\\2x=\dfrac{19\pi}{12}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{24}+k\pi\\x=\dfrac{19\pi}{24}+k\pi\end{matrix}\right.\)