Question

Inequality !

Answer 1

i step on this one while i was surfing the net... \[\large\ \frac{ (1 + xy + yz + xz)( 1 + 3x^2 + 3y^2 + 3z^2 }{ 9(x + y)(y + z)(x + z) }\ge (\frac{ x \sqrt{1 + x} }{ \sqrt[4]{3 + 9x^2} } + \frac{ y \sqrt{1 + y} }{ \sqrt[4]{3 + 9y^2} } + \frac{ z \sqrt{1 + z} }{ \sqrt[4]{3 + zx^2} } )^2\]

Answer 2

where
\[\large\ x , y , z > 0 \] and\[\large \ x + y + z = 1\]
ok.....now.. how can i prove this ?

Answer 3

@ganeshie8 @phi can u guys lend me a hand ?

Answer 4

\[\large\ \ge (\frac{ x \sqrt{1 + x} }{ \sqrt[4]{3 + 9x^2} } + \frac{ y \sqrt{1 + y} }{ \sqrt[4]{3 + 9y^2} } + \frac{ z \sqrt{1 + z} }{ \sqrt[4]{3 + 9z^2} } )^2\]

Answer 5

@iambatman & @ikram002p