1) Cho \(\frac{a^2}{b+c}+\frac{b^2}{a+c}+\frac{c^2}{a+b}=0\)
CM: \(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=1\)
2) Cho \(abc\ne1\)và \(\frac{ab+1}{b}=\frac{bc+1}{c}=\frac{ac+1}{a}\)
CM: a=b=c
Cho \(a.b.c\ne1;-1\)và \(\frac{ab+1}{b}=\frac{bc+1}{c}=\frac{ca+1}{a}\).
Cmr a=b=c
Cho abc = 1. CMR:
\(\frac{a}{ab+a+1}+\frac{b}{bc+b+1}+\frac{c}{ac+c+1}=1\)
Cho a+b+c=1 ( a,b,c khác 1 và 2 ) CMR: \(\frac{c+ab}{a^2+b^2+abc-1}+\frac{a+bc}{b^2+c^2+abc-1}+\frac{b+ac}{a^2+c^2+acb-1}=\frac{bc+ac+ab+8}{(a-2)(b-2)(c-2)}\)
cho M =\(\frac{b-c}{a^2-ac-ab+bc}+\frac{c-a}{b^2-ab-cb+ca}+\frac{a-b}{c^2-bc-ac+ab}\) và N=\(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\) cmr M=2N
CMR :
\(\frac{a-b}{1+ab}+\frac{b-c}{1+bc}+\frac{c-a}{1+ac}=\frac{a-b}{1+ab}-\frac{b-c}{1+bc}-\frac{c-a}{1+ac}\)
cho abc = 1
CMR \(\frac{b}{bc+b+1}\)+ \(\frac{a}{ab+a+1}\)+\(\frac{c}{ac+c+1}\)= 1
Cho a,b,c>0 và abc=1
CMR\(\frac{a}{ab+1}+\frac{b}{bc+1}+\frac{c}{ca+1}\ge\frac{3}{2}\)
Cho abc = 1.
CMR: \(\frac{a}{ab+a+1}\)= \(\frac{b}{bc+b+1}\)= \(\frac{c}{ac+c+1}\)= 3
