四元不等式

Let a = 1/(1+w) , b = 1/(1+x) , c = 1/(1+y) , d = 1/(1+z) , then a + b + c + d ≤ 1.
w x y z
= (1 - a)/a * (1 - b)/b * (1 - c)/c * (1 - d)/d
≥ (a+b+c+d - a)/a * (a+b+c+d - b)/b * (a+b+c+d - c)/c * (a+b+c+d - d)/d
= (b+c+d)/a * (a+c+d)/b * (a+b+d)/c * (a+b+c)/d
≥ 3∛(bcd) / a * 3∛(acd) / b * 3∛(abd) / c * 3∛(abc) / d
= 81