1.
Pt hoành độ giao điểm:
\(x^2+6=x^4-3x^2+1\)
\(\Leftrightarrow x^4-4x^2-5=0\Rightarrow\left[{}\begin{matrix}x^2=-1\left(l\right)\\x^2=5\end{matrix}\right.\)
\(\Rightarrow x=\pm\sqrt{5}\)
Đồ thị 2 hàm số đã cho có 2 điểm chung
2.
\(y'=1-2sin2x=0\Rightarrow sin2x=\frac{1}{2}\Rightarrow x=\frac{\pi}{12}\)
\(y\left(0\right)=1\) ; \(y\left(\frac{\pi}{4}\right)=\frac{\pi}{4}\) ; \(y\left(\frac{\pi}{12}\right)=\frac{\pi}{12}+\frac{\sqrt{3}}{2}\)
\(\Rightarrow y_{min}=y\left(\frac{\pi}{4}\right)=\frac{\pi}{4}\)
3.
\(\Leftrightarrow2^{2x-12}=2^{-x}\)
\(\Leftrightarrow2x-12=-x\)
\(\Leftrightarrow x=4\)
