cho a,b,c > 0 cmr: \(\frac{b^2a}{a^3\left(b+c\right)}+\frac{c^2a}{b^3\left(c+a\right)}+\frac{a^2b}{c^3\left(a+b\right)}\ge\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
Cho a,b,c là các số dương. CMR
\(\frac{a}{\sqrt{2b^2+2c^2-a^2}}+\frac{b}{\sqrt{2c^2+2a^2-b^2}}+\frac{c}{\sqrt{2a^2+2b^2-c^2}}\ge\sqrt{3}\)
Câu 1 : Cho a,b,c>0 thỏa mã ab+bc+ac=3. CMR : \(\frac{a}{2a^2+bc}+\frac{b}{2b^2+ac}+\frac{c}{2c^2+ab}\ge abc\)
Câu 2 : Cho a,b,c>0. CMR: \(\frac{2}{a}+\frac{6}{b}+\frac{9}{c}\ge\frac{8}{2a+b}+\frac{48}{3b+2c}+\frac{12}{c+3a}\)
\(\frac{b^2c^3}{a^2+\left(b+c\right)^3}+\frac{c^2a^3}{b^2+\left(c+a\right)^3}+\frac{a^2b^3}{c^2+\left(a+b\right)^3}\ge\frac{9abc}{4\left(3abc+a^2c+b^2a+c^2b\right)}\)voi a,b,c>0
Cho a,b,c > 0 thỏa mãn: ab + bc + ca = 3
CMR: \(\frac{a}{2a^2+bc}+\frac{b}{2b^2+ca}+\frac{c}{2c^2+ba}\ge abc\)
Cho a,b,c>0 chứng minh \(\frac{2a^2}{2b+c}+\frac{2b^2}{2a+c}+\frac{c^3}{4a+4b}\ge\frac{1}{4}\left(2a+2b+c\right)\)
1) cho a;b;c ko âm .chứng minh \(\sqrt{\frac{a+2b}{3}}+\sqrt{\frac{b+2c}{3}}+\sqrt{\frac{c+2a}{3}}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}\)
2) cho a;;b;c dương và abc=1. chứng minh \(\frac{bc}{a^2b+a^2c}+\frac{ca}{b^2c+b^2a}+\frac{ab}{c^2a+c^2b}\ge\frac{3}{2}\)
Cho a,b,c >0 và a+b+c=3
CMR: \(\frac{1}{\sqrt{2a+b+1}}+\frac{1}{\sqrt{2b+c+1}}+\frac{1}{\sqrt{2c+a+1}}\ge\frac{3}{2}\)
Cho a,b,c là các số dương thỏa mãn a+b+c=3. CMR
\(\frac{1}{2a^2+3}+\frac{1}{2b^2+3}+\frac{1}{2c^2+3}\ge\frac{3}{5}\)