a/(b+c-a)+b/(a+c-b)+c/(a+b-c)>=3
đặt:
A = b+c-a
B = a+c-b
C = b+a-c
=> a = (B+C)\2, b = (A+C)\2,c= (A+B)\2
== ====
ta có: (A\B + B\A) + (A\C + C\A) + (B\C+C\B) ≥ 6
=> (C+B)\A + (A+B)\C + (A+C)\B ≥ 6
=> 2a\(b+c-a) + 2b\(c+a-b) + 2c\(b+a-c) ≥ 6
=> đpcm
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Verified answer
đặt:
A = b+c-a
B = a+c-b
C = b+a-c
=> a = (B+C)\2, b = (A+C)\2,c= (A+B)\2
== ====
ta có: (A\B + B\A) + (A\C + C\A) + (B\C+C\B) ≥ 6
=> (C+B)\A + (A+B)\C + (A+C)\B ≥ 6
=> 2a\(b+c-a) + 2b\(c+a-b) + 2c\(b+a-c) ≥ 6
=> đpcm