User:Temperal/Inequalities
![\[\left(\sum_{sym}\frac {x}{y}\right)\left(\sqrt {(2x^2 + 2y^2 + 2z^2)(2x + 2y + 2z)}\right)\ge 1,x,y,z\in\mathbb{R}^ + ,x + y + z = \frac {1}{2}\]](http://latex.artofproblemsolving.com/7/3/9/739e32bd51bce1bd1c8a36ce74cdda3097065453.png)
![\[\sum_{cyc}\frac{a\sqrt{a^2+3bc}}{\sqrt{b+c}}\ge a + b + c,a,b,c\in \mathbb{R}^+\]](http://latex.artofproblemsolving.com/c/e/9/ce9942b9db8324ab89fcbefa3e995f4020277580.png)
\[\left(\sum_{sym} x\sqrt {y}\right)\left(\sum_{sym}\frac {x}{\sqrt {y}}}\right)\ge 1,\{x,y,z|x,y,z\in\mathbb{R}^{ + },x + y + z = \frac {1}{2}\}\] (Error compiling LaTeX. Unknown error_msg)
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