Question

Cho abc=1. CMR \(\dfrac{a}{ab}+a+1+\dfrac{b}{bc}+b+1+\dfrac{c}{ac}+c+1=1\)

Answer 1

Chắc bạn viết nhầm đề, cho \(a=b=c=1\) đâu có đúng

Sửa lại đề: cho \(abc=1\) chứng minh \(\dfrac{a}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{c}{ac+c+1}=1\)

Ta có

\(\dfrac{a}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{c}{ac+c+1}=\dfrac{a}{ab+a+1}+\dfrac{ab}{abc+ab+a}+\dfrac{c}{ac+c+abc}\)

\(=\dfrac{a}{ab+a+1}+\dfrac{ab}{1+ab+a}+\dfrac{c}{c\left(a+1+ab\right)}\)

\(=\dfrac{a}{ab+a+1}+\dfrac{ab}{ab+a+1}+\dfrac{1}{ab+a+1}\)

\(=\dfrac{a+ab+1}{ab+a+1}=1\) (đpcm)

Answer 2

Đề bạn Lâm đúng đấy!