\(Cho a,b,c>0. Cmr: \dfrac{a^3b}{1+ab^2}+\dfrac{b^3c}{1+bc^2}+\dfrac{c^3a}{1+ca^2}>\dfrac{abc(a+b+c)}{1+abc}\)
cho a,b,c là các số thực dương thỏa mãn \(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{a+c}=2017\)
Tìm max \(P=\dfrac{1}{2a+3b+3c}+\dfrac{1}{3a+2b+3c}+\dfrac{1}{3a+3b+2c}\)
cho a,b,c>0 thỏa mãn abc=1.CMR\(\dfrac{a^3}{1+b}+\dfrac{b^3}{1+c}+\dfrac{c^3}{1+a}\ge\dfrac{3}{2}\)
cho a,b,c>0 thỏa mãn abc=1.
CMR:\(\dfrac{a}{ab+1}+\dfrac{b}{bc+1}+\dfrac{c}{ca+1}\ge\dfrac{3}{2}\)
Cho a, b, c > 0 thỏa mãn : \(ab+bc+ca=3abc\)
Tìm GTLN : F = \(\dfrac{1}{a+2b+3c}+\dfrac{1}{2a+3b+c}+\dfrac{1}{3a+b+2c}\)
Cho 3 số thực dương a,b.c thỏa mãn abc=1 cmr:\(\dfrac{b+c}{\sqrt{a}}+\dfrac{c+a}{\sqrt{b}}+\dfrac{a+b}{\sqrt{c}}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}+3\)
Cho a, b, c khác 0 và \(a^3b^3+b^3c^3+c^3a^3=3a^2b^2c^2\)
Tính \(A=\left(1+\dfrac{a}{b}\right)\left(1+\dfrac{b}{c}\right)\left(1+\dfrac{c}{a}\right)\)
Cho a,b,c > 0. Cmr :
\(\dfrac{1}{a\left(1+b\right)}+\dfrac{1}{b\left(1+c\right)}+\dfrac{1}{c\left(1+a\right)}\ge\dfrac{3}{1+abc}\)
Biết a,b,c > 0 thỏa mãn ab+bc+ca=3abc
\(P=\dfrac{a}{\left(3a-1\right)^2}+\dfrac{b}{\left(3b-1\right)^2}+\dfrac{c}{\left(3c-1\right)^2}\) đạt min