a)cho a,b,c > 0 . Cmr: \(\left(a+b+c\right)^2\ge3\left(ab+bc+ca\right)\)
b)cho a,b,c > 0 thỏa mãn \(a^2+b^2+c^2=3\) . Cmr: \(\left(a^2b+b^2c+c^2a\right)\left(a+b+c\right)\ge9abc\)
cho a,b,c > 0 thỏa mãn ab+bc+ca=1. Cmr:
\(\left(a^2+2b^2+3\right)\left(b^2+2c^2+3\right)\left(c^2+2a^2+3\right)\ge64\)
cmr với mọi số thực a, b, c dươngta đều có bđt
\(\dfrac{a^2}{\left(2a+b\right)\left(2a+c\right)}+\dfrac{b^2}{\left(2b+a\right)\left(2b+c\right)}+\dfrac{a^2}{\left(2c+a\right)\left(2c+b\right)}\)<=3
CMR với mọi số nguyên a,b,c ta đều có BĐT:
\(\dfrac{a^2}{\left(2a+b\right)\left(2a+c\right)}+\dfrac{b^2}{\left(2b+a\right)\left(2b+c\right)}+\dfrac{c^2}{\left(2c+a\right)\left(2c+b\right)}\le\dfrac{1}{3}\)
cho a,b,c > 0 thỏa mãn a + b + c = 6abc.
Cmr: \(\frac{bc}{a^3\left(c+2b\right)}+\frac{ac}{b^3\left(a+2c\right)}+\frac{ab}{c^3\left(b+2a\right)}\ge2\)
cho a,b,c > 0 thỏa mãn a+b+c=6abc.
Cmr: \(\frac{bc}{a^3\left(c+2b\right)}+\frac{ca}{b^3\left(a+2c\right)}+\frac{ab}{c^3\left(b+2a\right)}\ge2\)
cho a,b,c> 0 . Cmr:
\(2\left(\frac{a}{b+2c}+\frac{b}{c+2a}+\frac{c}{a+2b}\right)\ge1+\frac{b}{b+2a}+\frac{c}{c+2b}+\frac{a}{a+2c}\)
cho các số thực dương a,b,c thỏa mãn \(\sqrt{a}+\sqrt{b}+\sqrt{c}=1\)
cmr \(\frac{a^2+bc}{\sqrt{2a^2\left(b+c\right)}}+\frac{b^2+ca}{\sqrt{2b^2\left(c+a\right)}}+\frac{c^2+ab}{\sqrt{2c^2\left(a+b\right)}}\ge1\)
Cho a,b,c là số dương thỏa mãn a+b+c=3. CMR
a/ \(8\left(a+b\right)\left(b+c\right)\left(c+a\right)\le\left(3+a\right)\left(3+b\right)\left(3+c\right)\)
b/ \(\left(3-2a\right)\left(3-2b\right)\left(3-2c\right)\le abc\)
