Lời giải:
Ta có:
\(y=5-\sin ^2x\cos ^2x=5-\frac{1}{4}(2\sin x\cos x)^2=5-\frac{1}{4}\sin^2 2x\)
Vì \(\sin 2x\in [-1;1], \forall x\in\mathbb{R}\Rightarrow \sin ^2x\in [0;1]\) hay \(0\leq \sin ^22x\leq 1\)
\(\Rightarrow 5-\frac{1}{4}.0\geq 5-\frac{1}{4}\sin ^22x\geq 5-\frac{1}{4}.1\)
\(\Leftrightarrow 5\geq y\geq \frac{19}{4}\)
Vậy \(\left\{\begin{matrix} y_{\max}=5\Leftrightarrow \sin 2x=0\\ y_{\min}=\frac{19}{4}\Leftrightarrow \sin 2x=\pm 1\end{matrix}\right.\)
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