Ta có: [tex]\frac{1}{x^2+yz}+\frac{1}{y^2+zx}+\frac{1}{z^2+xy}\leq \frac{1}{2x\sqrt{yz}}+\frac{1}{2y\sqrt{xz}}+\frac{1}{2z\sqrt{xy}}=\frac{1}{2}(\sqrt{\frac{1}{xy}.\frac{1}{xz}}+\sqrt{\frac{1}{xy}.\frac{1}{yz}}+\sqrt{\frac{1}{xz}.\frac{1}{yz}})\leq \frac{1}{2}[\frac{1}{2}(\frac{1}{xy}+\frac{1}{xz})+\frac{1}{2}(\frac{1}{xy}+\frac{1}{yz})+\frac{1}{2}(\frac{1}{xz}+\frac{1}{yz})]=\frac{1}{2}(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx})[/tex]