Question

Tìm nghiệm của pt:

1) \(2cos2x+\sqrt{2}cos\frac{\pi}{4}=0\) thuộc khoảng (0;2π)

2) \(sin4x-cos4x+\sqrt{2}cos\left(4x-\frac{\pi}{4}\right)=\sqrt{6}\) thuộc khoảng (-π;5π)

Answer 1

1.

\(\Leftrightarrow2cos2x+\sqrt{2}.\frac{\sqrt{2}}{2}=0\)

\(\Leftrightarrow cos2x=-\frac{1}{2}\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{3}+k\pi\\x=-\frac{\pi}{3}+k\pi\end{matrix}\right.\)

\(\Rightarrow x=\left\{\frac{\pi}{3};\frac{4\pi}{3};\frac{2\pi}{3};\frac{5\pi}{3}\right\}\)

2.

\(\Leftrightarrow sin4x-cos4x+sin4x+cos4x=\sqrt{6}\)

\(\Leftrightarrow2sin4x=\sqrt{6}\)

\(\Leftrightarrow sin4x=\frac{\sqrt{6}}{2}>1\)

Pt vô nghiệm