Các câu hỏi tương tự
Cho a,b,c>0 thỏa\(ab+ac+bc=0\)
CMR\(\frac{a^4}{b+3c}+\frac{b^4}{c+3a}+\frac{c^4}{a+3b}>hoặc=\frac{3}{4}\)
Bài 1 :Cho a,b,c dương thỏa mãn a+b+c=2
CMR \(\frac{bc}{\sqrt{3a^2+4}}+\frac{ca}{\sqrt{3b^2+4}}+\frac{ab}{\sqrt{3c^2+4}}\ge\frac{\sqrt{3}}{3}\)
Bài 2:Cho a,b,c>0. CMR
\(\left(a+b\right)\left(b+c\right)\left(c+a\right)\ge\frac{8}{9}\left(a+b+c\right)\left(ab+bc+ca\right)\)
Cho a,b,c>0 và a+b+c=2007. CMR:
\(\frac{5a^3-b^3}{ab+3a^2}+\frac{5b^3-c^3}{bc+3b^2}+\frac{5c^3-a^3}{ac+3c^2}\le2007\)
cho a;b;c >0. CMR:
\(P=\frac{5b^3-a^3}{ab+3b^2}+\frac{5c^3-b^3}{bc+3c^2}+\frac{5a^3-c^3}{ac+3a^2}\ge a+b+c\)
Cho a,b,c>0,tim GTNN:\(\frac{\sqrt{a^3c}}{\sqrt{b^3a}+bc}+\frac{\sqrt{b^3a}}{\sqrt{c^3b}+ac}+\frac{\sqrt{c^3b}}{\sqrt{a^3c}+ab}\)
Cho a,b,c lớn hơn 0
CMR : \(\frac{ab}{a+3b+2c}+\frac{bc}{b+3c+2a}+\frac{ac}{c+3a+2b}\le\frac{a+b+c}{6}\)
1,cho a,b,c>0 . CMR: \(\frac{b}{a+3b}+\frac{c}{b+3c}+\frac{a}{c+3a}\le\frac{3}{4}\)
2,CHo a,b,c>0 thỏa mãn a+b+c <= ab+bc+ca
CMR: \(\frac{1}{1+a+b}+\frac{1}{1+b+c}+\frac{1}{1+c+a}\le1\)
3, Cho a,b,c>0 thoaor mãn a+b+c=3
CMR: \(\frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge1\)
Dùng bđt bunhiacopxki nha
Với a,b,c > 0 và a+b+c =3 CMR : \(\frac{a+3}{3a+bc}+\frac{b+3}{3b+ca}+\frac{c+3}{3c+ab}\ge3\)
cho a,b,c>0
cmr \(\frac{5a^3-b^3}{ab+3b^2}+\frac{5b^3-c^3}{cb+3c^2}+\frac{5c^3-a^3}{ac+3a^2}\le a+b+c\)