câu 1 :Cmr a)\(\frac{a^2+b^2}{2}\ge\left(\frac{a+b}{2}\right)^2\)
b) \(\frac{a^3+b^3+c^3}{3}\ge\left(\frac{a+b+c}{3}\right)^3\)
câu 2 : cho a+b=1 .Cm \(\frac{1}{a+1}+\frac{1}{b+1}\ge\frac{4}{3}\)
câu 3: cho a+b+c=1và a,b,c>0.CMR \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge9\)
câu 4 Tim max của : ab+2(a+b) ...biết a2+b2=1
giúp mik
câu 1 :Cmr a)\(\frac{a^2+b^2}{2}\ge\left(\frac{a+b}{2}\right)^2\)
b) \(\frac{a^3+b^3+c^3}{3}\ge\left(\frac{a+b+c}{3}\right)^3\)
câu 2 : cho a+b=1 .Cm \(\frac{1}{a+1}+\frac{1}{b+1}\ge\frac{4}{3}\)
câu 3: cho a+b+c=1và a,b,c>0.CMR \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge9\)
câu 4 Tim max của : ab+2(a+b) ...biết a2+b2=1
cho a,b,c>0
Cm: \(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{2\sqrt[3]{abc}}\ge\frac{\left(a+b+c+\sqrt[3]{abc}\right)^2}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\)
cho \(\left\{{}\begin{matrix}a,b,c>0\\a+b+c=3\end{matrix}\right.\). CMR: \(\frac{a+b}{1+a}+\frac{b+c}{1+b}+\frac{c+a}{1+c}\ge ab+bc+ca\)
cho 0< a,b,c < 2 . Cmr: \(\frac{1}{2-a}+\frac{1}{2-b}+\frac{1}{2-c}\ge\frac{a^2+b^2+c^2}{2}+\frac{3}{2}\)
cho \(\left\{{}\begin{matrix}a,b,c>0\\a+b+c=1\end{matrix}\right.\). chứng minh:\(2\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right)\ge\frac{1+a}{1-a}+\frac{1+b}{1-b}+\frac{1+c}{1-c}\)
cho a,b,c>0 và a+b+c=1
Tìm GTNN của \(A=\frac{a^3}{\left(1-a\right)^2}+\frac{b^3}{\left(1-b\right)^2}+\frac{c^3}{\left(1-c\right)^2}\)
cho a,b,c>0 thỏa mãn a+b+c=1
Cmr: \(\frac{1}{a+b^2}+\frac{1}{b+c^2}+\frac{1}{c+a^2}\le\frac{1}{4}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
cho a,b,c>0. CMR: \(\frac{1}{a\sqrt{a+b}}+\frac{1}{b\sqrt{b+c}}+\frac{1}{c\sqrt{c+a}}\ge\frac{3}{\sqrt{2abc}}\)
cho a,b,c>0 và abc=1
Cmr: \(\frac{1}{\left(a+1\right)^2+b^2+1}+\frac{1}{\left(b+1\right)^2+c^2+1}+\frac{1}{\left(c+1\right)^2+a^2+1}\le\frac{1}{2}\)