x.y.z都大于0,xy+yz+xz=1,求1/(x+y)+1/(x+z)+1/(y+z)的最小值

题目

x.y.z都大于0,xy+yz+xz=1,求1/(x+y)+1/(x+z)+1/(y+z)的最小值

答案

将x y 设定为0:0.01:100（范围0-100,步长0.01）,用matlab算了一下,给出的最小结果是 0.044996,以下是Matlab程序,凑合着看看能用不.
for x = 0:0.01:100
for y = 0:0.01:100
z = (1-x.*y)./(x+y);
t = 1./(x+y) + 1./(x+z)+1./(y+z);
end
end
min(t)