I managed to solve the following inequality using AM-GM:
a(a+1)(b+1)+b(b+1)(c+1)+c(c+1)(a+1)≥34
provided that a,b,c>0 and abc=1.
However it was hinted to me that this could also be solved with Cauchy-Schwarz inequality but I have not been able to find a solution using it and I'm really out of ideas.
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