Cho a, b, c > 0 . CMR:
\(\frac{1}{a+b+c}\ge\frac{a^3}{\left(2a^2+b^2\right)\left(2a^2+c^2\right)}+\frac{b^3}{\left(2b^2+c^2\right)\left(2b^2+a^2\right)}+\frac{c^3}{\left(2c^2+a^2\right)\left(2c^2+a^2\right)}\)
Cho a,b,c>0. Chứng minh: \(\frac{1}{2a+b+c}+\frac{1}{a+2b+c}+\frac{1}{a+b+2c}\)\(\ge\frac{9}{4a+4b+4c}\)
Cho a+b-c=0 đặt A=\(\dfrac{4bc-a^2}{-bc+2a^2}\)
B=\(\dfrac{4ac-b^2}{2b^2-ac}\) , C=\(\dfrac{4ab-c^2}{ab+2c^2}\)
CM:A.B.C=1
Cho số thực dương a,b,c thỏa mãn a+b+c=2016.
Tìm min biểu thức P = \(\frac{2a+3b+3c+1}{2015+a}+\frac{3a+2b+3c}{2016+b}+\frac{3a+3b+2c-1}{2017+c}\)
Cho a, b, c > 0 thỏa mãn: \(\frac{2}{b}=\frac{1}{a}+\frac{1}{c}\)
Tìm \(minP=\frac{a+b}{2a-b}+\frac{c+b}{2c-b}\)
Cho a, b, c > 0. CMR :
\(\frac{a^2+b^2}{2c}+\frac{b^2+c^2}{2a}+\frac{c^2+a^2}{2b}\le\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\)
Cho a, b, c > 0. Chứng minh rằng :
\(a+b+c\le\frac{a^2+b^2}{2c}+\frac{b^2+c^2}{2a}+\frac{c^2+a^2}{2b}\le\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}\)
Cho a, b, c là các số thực dương. CMR:
\(\frac{ab}{a+3b+2c}+\frac{bc}{b+3c+2a}+\frac{ca}{c+3a+2b}< \frac{a+b+c}{6}\)
Cho a, b, c > 0. Chứng minh rằng :
\(a+b+c\le\frac{a^2+b^2}{2c}+\frac{b^2+c^2}{2a}+\frac{c^2+a^2}{2b}\)