Let
![w, x, y, z](/media/m/e/4/6/e46dd38573fcbfad752112ec556e0b86.png)
are non-negative reals such that
![wx + xy + yz + zw = 1](/media/m/2/1/f/21f770506292fade7511ed234a9fbb8c.png)
. Show that
![\frac {w^3}{x + y + z} + \frac {x^3}{w + y + z} + \frac {y^3}{w + x + z} + \frac {z^3}{w + x + y}\geq \frac {1}{3}](/media/m/4/c/8/4c873f953fca8e23e174899fa5090807.png)
.
%V0
Let $w, x, y, z$ are non-negative reals such that $wx + xy + yz + zw = 1$. Show that
$$\frac {w^3}{x + y + z} + \frac {x^3}{w + y + z} + \frac {y^3}{w + x + z} + \frac {z^3}{w + x + y}\geq \frac {1}{3}$$.