a,b,c都大于0,且a+b+c=1,求1/(a+b)+1/(b+c)+1/(a+c)的最小值
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![a,b,c都大于0,且a+b+c=1,求1/(a+b)+1/(b+c)+1/(a+c)的最小值](/uploads/image/z/5441369-41-9.jpg?t=a%2Cb%2Cc%E9%83%BD%E5%A4%A7%E4%BA%8E0%2C%E4%B8%94a%2Bb%2Bc%3D1%2C%E6%B1%821%2F%28a%2Bb%29%2B1%2F%28b%2Bc%29%2B1%2F%28a%2Bc%29%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC)
a,b,c都大于0,且a+b+c=1,求1/(a+b)+1/(b+c)+1/(a+c)的最小值
a,b,c都大于0,且a+b+c=1,求1/(a+b)+1/(b+c)+1/(a+c)的最小值
a,b,c都大于0,且a+b+c=1,求1/(a+b)+1/(b+c)+1/(a+c)的最小值
a>0、b>0、c>0,且a+b+c=1
∴1/(a+b)+1/(b+c)+1/(c+a)
=1²/(a+b)+1²/(b+c)+1²/(c+a)
≥(1+1+1)²/[(a+b)+(b+c)+(c+a)]
=9/[2(a+b+c)]
=9/2.
故所求最小值为:9/2.