Question

Giải các phương trình:

a) sin²x-5sinx+4=0

b) 2cos²2x-3cos2x+1=0

c) sin²3x-\(\frac{3}{2}\)sin3x+1=0

Answer 1

a/

\(\Leftrightarrow\left(sinx-1\right)\left(sinx-4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}sinx=1\\sinx=4\left(vn\right)\end{matrix}\right.\) \(\Rightarrow x=\frac{\pi}{2}+k2\pi\)

b/

\(\Leftrightarrow\left(cos2x-1\right)\left(2cosx-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}cosx=1\\cosx=\frac{1}{2}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=k2\pi\\x=\pm\frac{\pi}{3}+k2\pi\end{matrix}\right.\)

c/

\(\Leftrightarrow\left(sin3x-\frac{3}{4}\right)^2+\frac{7}{16}=0\)

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