a+b+c=1
(a+b+c)^2 = 1
a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = 1..........(1)
又因为(a - b)^2 + (b - c)^2 +(a - c)^2 >= 0
a^2 + b^2 + c^2 >= ab + bc + ac ..............(2)
把(2)代入(1)得
3(ab + bc + ac )<= a^2 + b^2 + c^2 + 2ab + 2bc + 2ac = 1
即 3(ab + bc + ac )<= 1
则 ab + bc + ac <= 1/3
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