Question 75
If $x, y, z, t \gt 0$ and $x + y + z + t = 1$
$$
\frac{xy(z+t)}{1-4zt} + \frac{yz(t+x)}{1-4tx} + \frac{zt(x+y)}{1-4xy} + \frac{tx(y+z)}{1-4yz} \ge \frac{128}{3}xyzt
$$
$$
\frac{xy(z+t)}{1-4zt} + \frac{yz(t+x)}{1-4tx} + \frac{zt(x+y)}{1-4xy} + \frac{tx(y+z)}{1-4yz} \ge \frac{128}{3}xyzt
$$