Từ a.b.c=1 ta có:
\(\dfrac{a}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{c}{ca+c+1}=\dfrac{a}{ab+a+abc}+\dfrac{b}{bc+b+1}+\dfrac{c}{ca+c+1}=\dfrac{a}{a\left(b+1+bc\right)}+\dfrac{b}{bc+b+1}+\dfrac{c}{ca+c+1}=\dfrac{b+1}{b+abc+bc}+\dfrac{c}{ca+c+1}=\dfrac{b+1}{b\left(1+ac+c\right)}+\dfrac{c}{ac+c+1}=\dfrac{b+1+bc}{b\left(1+ac+c\right)}=\dfrac{bc+b+1}{bc+b+abc}=\dfrac{bc+b+1}{bc+b+1}=1\)
Cho a,b,c >0. Chứng minh rằng
\(\dfrac{1}{a^2+bc}+\dfrac{1}{b^2+ac}+\dfrac{1}{c^2+ab}\le\dfrac{a+b+c}{2abc}\)
chứng minh
\(\dfrac{1+ab}{a-b}.\dfrac{1+bc}{b-c}+\dfrac{1+bc}{b-c}.\dfrac{1+ca}{c-a}+\dfrac{1+ca}{c-a}.\dfrac{1+ab}{a-b}=1\)
Cho a, b, c > 0 .CMR: \(\dfrac{ab}{a+b}+\dfrac{bc}{b+c}+\dfrac{ac}{a+c}\) ≤ \(\dfrac{1}{2}\)
Cho a, b, c > 0 .CMR: \(\dfrac{ab}{a+b}+\dfrac{bc}{b+c}+\dfrac{ac}{a+c}\) ≤ \(\dfrac{1}{2}\left(a+b+c\right)\)
Cho a,b,c là các số thực dương thỏa mãn \(a+b+c=1\)
chứng minh rằng \(\dfrac{ab+c}{c+1}+\dfrac{bc+a}{a+1}+\dfrac{ac+b}{b+1}\le1\)
Cho a.b.c=1
CMR \(\dfrac{1}{1+ab}+a+\dfrac{1}{1+bc}+b+\dfrac{1}{1+ac}+c=1\)
Cho a.b.c=1
CMR \(\dfrac{1}{1+ab}+a+\dfrac{1}{1+bc}+b+\dfrac{1}{1+ac}+c=1\)
bài 1: cho abc=2006
tính A=
\(\dfrac{a}{ab+a+2006}+\dfrac{b}{bc+b+1}+\dfrac{2006c}{ac+2006c+2006}\)
bài 2:a,b,c thỏa mãn \(a^3+b^3+c^3\)=3abc
tính N=\(\left(1+\dfrac{a}{b}\right).\left(1+\dfrac{b}{c}\right).\left(1+\dfrac{c}{a}\right)\)
Cho a,b,c khác 0 thỏa mãn \(\left(1+\dfrac{b}{a}\right)\left(1+\dfrac{c}{b}\right)\left(1+\dfrac{a}{c}\right)=8\)
CMR \(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}=\dfrac{3}{4}+\dfrac{ab}{\left(a+b\right)\left(b+c\right)}+\dfrac{bc}{\left(b+c\right)\left(c+a\right)}+\dfrac{ca}{\left(c+a\right)\left(a+b\right)}\)
