Question

Câu 2)

a) 3cos²x - 2cosx + 1= 0

b) 25sin²x +15sin2x + 9cos²x =25

Answer 1

a/ Cái đầu tiên vô nghiệm rồi :v

b/ \(\Leftrightarrow\left(5\sin x\right)^2+5.3.2\sin x\cos x+\left(3\cos x\right)^2=25\)

\(\Leftrightarrow\left(5\sin x+3\cos x\right)^2=25\Leftrightarrow\left[{}\begin{matrix}5\sin x+3\cos x=5\\5\sin x+3\cos x=-5\end{matrix}\right.\)

Xét \(5\sin x+3\cos x=5\)

\(\cos\frac{x}{2}=0\Rightarrow x=\pi+k2\pi\)

\(\cos\frac{x}{2}\ne0\Leftrightarrow x\ne\pi+k2\pi\)

Đặt \(t=\tan\frac{x}{2}\Rightarrow\left\{{}\begin{matrix}\sin x=\frac{2t}{1+t^2}\\\cos x=\frac{1-t^2}{1+t^2}\end{matrix}\right.\)

\(\Rightarrow5\frac{2t}{1+t^2}+3.\frac{1-t^2}{1+t^2}=5\)

\(\Leftrightarrow8t^2-10t+2=0\) <tự giải nha, trường hợp 2 tương tự :)>