cho a,b,c khac nhau doi mot va 1/a+1/b+1/c=0.rut gon cac bieu thuc
N=bc/a^2+2bc+CA/B^2+2AC+AB/C^2+2AB
Cho a, b,c khác 0 thỏa: 1/a + 1/b+ 1/c =0, đặt P=bc-ac/ab+ac-ab/bc+ab-bc/ac , Q=bc/ac-ab+ca/ab-bc+ab/bc-ca. Tính P.Q
Cho a,b,c tung doi 1 khac nhau thoa man: ab+bc+ac=1
Tinh: A= [(a+b)2 (b+c)2 (a+c)2] / [(1+a2)(1+b2)(1+c2)]
Giai va bien luan cac phuong trinh sau:
1. \(\frac{a+b-x}{c}+\frac{a+c-x}{b}+\frac{b+c-x}{a}+\frac{4x}{a+b+c}=1\)
(an x) voi dk; a,b,b khac 0 va a+b+c khac 0
2.\(\frac{x-a}{bc}+\frac{x-b}{ac}+\frac{x-c}{ab}=2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
(an x) voi dk: a,b,c khac 0
3, \(\frac{mx+3}{6}+\frac{m^2-1}{2}=\frac{x+5}{10}+\frac{2}{5}\left(x+m^2+1\right)\)
(an x)
Cho a,b >0 sao cho a+b+c=1 CMR \(\frac{ab}{c+1}+\frac{bc}{a+1}+\frac{ac}{b+1}\le\frac{1}{4}\)
a, b, c \(\ge\)0; \(\frac{a}{1+bc}+\frac{b}{1+ac}+\frac{c}{1+ab}=3\). CM: \(\frac{a}{1+a+bc}+\frac{b}{1+b+ac}+\frac{c}{1+c+ab}\ge\frac{3}{4}\)
cho a,b,c duong , a+b+c=1
a, tim Min A=1/(a^2+b^2) +1/(b^2+c^2) +1/(c^2+a^2) +1/ab +1/bc +1/ac
b, tìm Min B=1/(a^2+bc) +1/(b^2+ac) +1/(c^2+ab) +1/ab +1/bc +1/ac
Cho a+b+c=0 .Tính
A=[ab.(a-b)+bc.(b-c)+ac(c-a)].[\(\frac{1}{ab.\left(a-b\right)}+\frac{1}{bc.\left(b-c\right)}+\frac{1}{ca.\left(c-a\right)}\)]
cho abc khac 1 va -1 va [ab+1]/b=[bc+1]/c=[ca+1]/a.chung minh a=b=c
