you've forgot
we have
\(\frac{2a}{a^2+c+1}\le\frac{2a}{2a+c}=1-\frac{c}{2a+c}=1-\frac{c^2}{2ac+c^2}\)
you've forgot
we have
\(\frac{2a}{a^2+c+1}\le\frac{2a}{2a+c}=1-\frac{c}{2a+c}=1-\frac{c^2}{2ac+c^2}\)
ten ten ten
1. Cho a,b,c>0 và a+b+c=1 CMR sigma\(\frac{a-bc}{a+bc}\le\frac{3}{2}\)
2. cho a,b,c>0 va abc=1 CMR sigma\(\frac{1}{a\left(b+1\right)}\ge\frac{3}{2}\)
3.(i think it is difficult for you)
ch a,b,c>0 CMR sigma\(\frac{b^2c^3}{a^2+\left(b+c\right)^3}\ge\frac{9abc}{4\left(3abc+ab^2+bc^2+ca^2\right)}\)
4. CMR với mọi n là số tự nhiên lớn hơn 1 thì \(\frac{1}{\sqrt{n^2+1}}+\frac{1}{\sqrt{n^2+2}}+...+\frac{1}{\sqrt{n^2+n}}< 1\)
Bai 1:Cho a,b,c>0 CMR
\(|\Sigma \frac{a^3-b^3}{a+b}| \leq \frac{\Sigma(a-b)^2}{4}\)
Bai 2 :Cho \(a,b,c \in R\) CMR
\(\Sigma \sqrt{a^2+(1-b)^2} \geq \frac{3}{\sqrt{2}}\)
Cho \(\frac{a}{c}=\frac{a-b}{b-c}\); a#0 ; c#0; a-b#0; b-c#0.
Chứng minh: \(\frac{1}{a}+\frac{1}{a-b}=\frac{1}{b-c}-\frac{1}{c}\)
Please help me !!!!!!!!!!!!!!!!!!!!!!!!!
cho a, b, c >0 và abc=1. CMR
\(\frac{a^2}{a^2+b^5+c^5}+\frac{b^2}{b^2+a^5+c^5}+\frac{c^2}{c^2+a^5+b^5}\le1\)
Cho a,b,c > 0 và abc = 1
CMR \(\Sigma\frac{1}{2a^3+b^3+c^3+2}\le\frac{1}{2}\)
Chờ a,b,c > 0 và ab + bc + ca = 2abc
CMR: \(sigma\frac{1}{a\left(2a-1\right)^2}\ge\frac{1}{2}\)
1,cho a,b,c>0 . CMR: \(\frac{b}{a+3b}+\frac{c}{b+3c}+\frac{a}{c+3a}\le\frac{3}{4}\)
2,CHo a,b,c>0 thỏa mãn a+b+c <= ab+bc+ca
CMR: \(\frac{1}{1+a+b}+\frac{1}{1+b+c}+\frac{1}{1+c+a}\le1\)
3, Cho a,b,c>0 thoaor mãn a+b+c=3
CMR: \(\frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge1\)
Dùng bđt bunhiacopxki nha
Cho \(a,b,c>0\)
CMR: \(\frac{1+\sqrt{3}}{3\sqrt{3}}\left(a^2+b^2+c^2\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge a+b+c+\sqrt{a^2+b^2+c^2}\)
HELP ME
cho a;b;c>0.CMR:\(\frac{a}{c+2a}+\frac{b}{a+2b}+\frac{c}{b+2c}\le1\)