Cho a,b,c > 0 thỏa mãn a + b + c = 1
CMR \(\frac{1}{a^2+b^2+c^2}+\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\ge30\)
Cho a;b;c > 0 thỏa mãn a + b + c = 1
CMR: \(\frac{ab}{a^2+b^2}+\frac{bc}{b^2+c^2}+\frac{ca}{c^2+a^2}+\frac{1}{4}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge\frac{15}{4}\)
Cho a, b, c > 0 thỏa mãn ab + bc + ca = 3. CMR :
\(\frac{1}{a^2+1}+\frac{1}{b^2+1}+\frac{1}{c^2+1}\ge\frac{3}{2}\)
Cho a,b,c >0 thỏa mãn abc=1. CMR: \(\frac{a}{ab+1}+\frac{b}{bc+1}+\frac{c}{ca+1}\ge\frac{3}{2}\)
cho a,b,c > 0 thỏa mãn abc=1.CMR
\(\frac{a}{ab+1}+\frac{b}{bc+1}+\frac{c}{ca+1}\ge\frac{3}{2}\)
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
a,b,c>0 thỏa mãn ab+bc+ca=1
CMR \(\frac{1}{1+a^2+b^2}+\frac{1}{1+b^2+c^2}+\frac{1}{1+c^2+a^2}\) bé hơn hoặc bằng 1
Cho các số dương a, b, c thỏa mãn ab+bc+ca=1.
CMR: \(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}\ge3+\sqrt{\frac{\left(a+b\right)\left(a+c\right)}{a^2}}+\sqrt{\frac{\left(b+c\right)\left(b+a\right)}{b^2}}+\sqrt{\frac{\left(c+a\right)\left(c+b\right)}{c^2}}\)
Cho a,b,c > 0 thỏa mãn a+b=3-c . CMR:
\(a^3+b^3+c^3+2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge3\left(ab+bc+ca\right)\)