If -LSB- math -RSB- a , b , c \ gt 0 -LSB- / math -RSB- and -LSB- math -RSB- abc = 1 -LSB- / math -RSB- , how can I prove that -LSB- math -RSB- -LRB- a +2 -RRB- -LRB- b +3 -RRB- -LRB- c +6 -RRB- \ ge 48 ? -LSB- / math -RSB-
How does one prove for -LSB- math -RSB- a , b , c \ ge 0 -LSB- / math -RSB- that -LSB- math -RSB- a ^ 3 + b ^ 3 + c ^ 3 \ ge 3abc -LSB- / math -RSB- ?