Đáp án:27.A 30.C 31.C
Giải thích các bước giải:
$\begin{array}{l}
27.{x^2} - x - 2 \ge 0\\
\Rightarrow \left[ \begin{array}{l}
x \ge 2\\
x \le - 1
\end{array} \right. \Rightarrow A\\
30.{\mathop{\rm s}\nolimits} {\rm{inx}} + 4\cos x = 2 + \sin 2x\\
\Rightarrow {\mathop{\rm s}\nolimits} {\rm{inx}} + 4\cos x - 2 - 2\sin x.c{\rm{osx = 0}}\\
\Rightarrow \left( {{\mathop{\rm s}\nolimits} {\rm{inx}} - 2} \right)\left( {1 - 2\cos x} \right) = 0\\
\Rightarrow c{\rm{osx = }}\frac{1}{2} \Rightarrow \left[ \begin{array}{l}
x = \frac{\pi }{3} + k2\pi \\
x = \frac{{ - \pi }}{3} + k2\pi
\end{array} \right. \Rightarrow C\\
31.\\
I = {\sin ^4}x + c{\rm{o}}{{\rm{s}}^4}x\\
= {\sin ^4}x + 2{\sin ^2}x.co{s^2}x + c{\rm{o}}{{\rm{s}}^4}x - 2{\sin ^2}x.co{s^2}x\\
= {\left( {{{\sin }^2}x + c{\rm{o}}{{\rm{s}}^2}x} \right)^2} - 2{\sin ^2}x.co{s^2}x\\
= 1 - \frac{1}{2}{\sin ^2}2x = 1 - \frac{1}{2}.\frac{{1 - c{\rm{os4x}}}}{2}\\
= 1 - \frac{1}{2}.\frac{1}{2}.\left( {1 - 1} \right) = 1 \Rightarrow C
\end{array}$
