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[不等式] 三元不等式

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v6mm131 posted 2017-8-31 21:25 |Read mode
若$ x, y, z >0 $,证明:$ \dfrac{3}{2(x+y+z)} \le \sum \dfrac{1}{3(y+z)+(\sqrt{x+y}-\sqrt{x+z})^2} $

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original poster v6mm131 posted 2017-8-31 21:28
若$ x, y, z >0 $,证明:
\[{\it \sum} \left( {\frac {x}{y+z+ \left( 1+\frac{2}{3}\,\sqrt {2} \right)
\left( \sqrt {x+y}-\sqrt {z+x} \right) ^{2}}} \right) \geq \frac{3}{2}\]

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