Cho $x\,,\,y\,,\,z\,>\,0$, $x\,+\,y\,+\,z\,=\,3$. Chứng minh rằng:
\[x\,+\,{x}^{\,-1}\,\geq\,1\,/\,4\, \left( \,x\,+\,yz \,\right) ^{\,2}+\,\,1\]
Cho $x\,,\,y\,,\,z\,>\,0$, $x\,+\,y\,+\,z\,=\,3$. Chứng minh rằng:
\[x\,+\,{x}^{\,-1}\,\geq\,1\,/\,4\, \left( \,x\,+\,yz \,\right) ^{\,2}+\,\,1\]
\[(\,z\,-\,x\,)^{\,2}+(\,1\,-\,y\,)^{\,2}\,\geq \,2\,(\,1\,-\,z\,)^{\,2}\]
\[|\,y\,-\,z\,|\,+\,|\,x\,-\,1\,|\,\geq\, 2\,|\,z\,-\,1\,|\]
\[1\,+\,\frac{\,y}{\,z\,+\,x\,}\,\geq \,\frac{\,3}{\,8}(\,x\,+\,y\,)(\,y\,+\,z\,)\]
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