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You should be able to take it from here, no doubt?  If you are not able to, nudge me. edit: Here is the complete solution. if a,b,c restricted to positive values less than 1 then
a=1-x, b = 1-y, c=1-z ;0 < x,y,z < 1 give
where x+y+z=1
hence,
and as each factor is of the form
Equality holds when x=y=z = 1/3 when a=2/3, b=2/3, and c=2/3
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