3. Áp dụng bdt cauchy$xt+xy+z+yzt\geq 4.\sqrt[4]{xtxyzyzt}=4\sqrt[4]{(xyzt)^2}=4\sqrt{xyzt}$$1\geq 4\sqrt{xyzt}\Leftrightarrow \sqrt{xyzt}\leq \frac{1}{4}\Leftrightarrow xyzt\leq \frac{1}{16}$$\Rightarrow K\leq \frac{1}{16}$vậy $K_{max}=\frac{1}{16}$ tại $y=t=1;x=z=\frac{1}{4}$
3. Áp dụng bdt cauchy$xt+xy+z+yzt\geq 4.\sqrt[4]{xtxyzyzt}=4\sqrt[4]{(xyzt)^2}=4\sqrt{xyzt}$$1\geq 4\sqrt{xyzt}\Leftrightarrow \sqrt{xyzt}\leq \frac{1}{4}\Leftrightarrow xyzt\leq \frac{1}{16}$$\Rightarrow K\leq \frac{1}{16}$vậy $K_{max}=\frac{1}{16}$ tại $x=y=t=1;z=\frac{1}{4}$
3. Áp dụng bdt cauchy$xt+xy+z+yzt\geq 4.\sqrt[4]{xtxyzyzt}=4\sqrt[4]{(xyzt)^2}=4\sqrt{xyzt}$$1\geq 4\sqrt{xyzt}\Leftrightarrow \sqrt{xyzt}\leq \frac{1}{4}\Leftrightarrow xyzt\leq \frac{1}{16}$$\Rightarrow K\leq \frac{1}{16}$vậy $K_{max}=\frac{1}{16}$ tại $y=t=1;
x=z=\frac{1}{4}$