Question

[Cristiano Ronaldo]

cho 3 số a,b,c thõa mãn : a.b.c=1

C/M : \(\frac{1}{ab+a+1}+\frac{b}{bc+b+1}+\frac{1}{abc+bc+b}=1\)1

Answer 1

[Nguyễn Anh Quân]

Có : 1/ab+a+1 = abc/ab+a+abc = bc/b+1+bc

1/abc+bc+b  = 1/1+bc+b

=> 1/ab+a+1 + b/bc+b+1 + 1/abc+bc+b = bc/bc+c+1 + b/bc+b+1 + 1/bc+b+1 = bc+b+1/bc+b+1 = 1

=> ĐPCM

k mk nha

Answer 2

[Phạm Tuấn Đạt]

Có : 1/ab+a+1 = abc/ab+a+abc = bc/b+1+bc

1/abc+bc+b  = 1/1+bc+b

=> 1/ab+a+1 + b/bc+b+1 + 1/abc+bc+b = bc/bc+c+1 + b/bc+b+1 + 1/bc+b+1 = bc+b+1/bc+b+1 = 1

=> ĐPCM