$y=\sin^4\dfrac{x}{2}+\cos^4\dfrac{x}{2}-\sin^2\dfrac{x}{2}\cos^2\dfrac{x}{2}$
$=\Big( \sin^2\dfrac{x}{2}+\cos^2\dfrac{x}{2}\Big)^2-3\sin^2\dfrac{x}{2}\cos^2\dfrac{x}{2}$
$=1-\dfrac{3}{4}\sin^2x$
Có: $0\le \sin^2x\le 1$
$\to \dfrac{-3}{4}\le -\dfrac{3}{4}\sin^2x\le 0$
$\to \dfrac{1}{4}\le y\le 1$
Vậy:
$\max y=1\to \sin^2x=0\to x=k\pi$
$\min y=\dfrac{1}{4}\to \sin^2x=1\to \cos x=0\to x=\dfrac{\pi}{2}+k\pi$
