BÊT ®¼NG THØC ®· CHO T−¬NG ®−¬NG VÍI 1(A B C)LG(ẠB.C) A LGA B LG B...

2) BÊt ®¼ng thøc ®· cho t−¬ng ®−¬ng víi

1

(a b c)lg(ạb.c) a lga b lg b clg c

3

+ +

+

+

⇔ 3(alga + blgb + clgc) − (a + b + c)(lga + lgb + lgc) ≥ 0

⇔ (a -b) (lga − lgb) + (a − c)(lga − lgc) + (b − c)(lgb − lgc) ≥ 0.

V× hµm lgx ®ång biÕn nªn nÕu a ≥ b > 0 th× lga ≥ lgb. Do ®ã

(a − b)(lga − lgb) ≥ 0. Tõ ®ã ta thÊy bÊt ®¼ng thøc cuèi cïng ®óng.

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