Dễ dàng CM đc:
tanA.tanB.tanC=tanA+tanB+tanCtheo BĐT Cauchy có: P=tan6A+tan6B+tan6C≥3.3√(tanA.tanB.tanC)6=3.(tanA.tanB.tanC)2
Mà: tanA+tanB+tanC≥3.3√tanA.tanB.tanC
=> (tanA+tanB+tanC)3≥27.tanA.tanB.tanC
=> (tanA+tanB+tanC)2≥27(do tanA+tanB+tanC=tanA.tanB.tanC)
=> tanA+tanB+tanC≥3√3
=> P≥3.(3√3)2=81 (đpcm)