Đặt \(sinx-cosx=\sqrt{2}sin\left(x-\dfrac{\pi}{4}\right)=t\) với \(\left|t\right|\le\sqrt{2}\)
\(\Rightarrow sin2x=1-t^2\)
Pt trở thành:
\(1-t^2+2\sqrt{2}t-3=0\)
\(\Leftrightarrow t^2-2\sqrt{2}t+2=0\)
\(\Leftrightarrow t=\sqrt{2}\)
\(\Leftrightarrow\sqrt{2}sin\left(x-\dfrac{\pi}{4}\right)=\sqrt{2}\)
\(\Leftrightarrow sin\left(x-\dfrac{\pi}{4}\right)=1\)
\(\Leftrightarrow x-\dfrac{\pi}{4}=\dfrac{\pi}{2}+k2\pi\)
\(\Leftrightarrow x=\dfrac{3\pi}{4}+k2\pi\)
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