Các câu hỏi tương tự
Giả sử \(0< a;b;c\le1\). CMR
\(\frac{a\left(b+c\right)}{bc\left(a+1\right)}+\frac{b\left(c+a\right)}{ca\left(b+1\right)}+\frac{c\left(a+b\right)}{ab\left(c+1\right)}\ge\frac{6}{1+\sqrt[3]{abc}}\)
cho a,b,c là các số thực dương thỏa mãn abc=1.CMR
\(\left(a-1+\frac{1}{b}\right)\left(b-1+\frac{1}{c}\right)\left(c-1+\frac{1}{a}\right)\le1\)
Cho a,c,b \(\in\left[0;1\right]\)Chứng minh rằng :\(\frac{a}{b+c+1}+\frac{b}{a+c+1}+\frac{c}{a+b+1}+\left(1-a\right)\left(1-b\right)\left(1-c\right)\le1\)
Cho các số thực dương a,b,c. CMR:
\(\left(a+\frac{1}{b}-1\right)\left(b+\frac{1}{c}-1\right)+\left(b+\frac{1}{c}-1\right)\left(c+\frac{1}{a}-1\right)+\left(c+\frac{1}{a}-1\right)\left(a+\frac{1}{b}-1\right)\ge3\)
Cho a, b, c > 0 và a + b + c = 3. CMR: \(\frac{a^3}{\left(a+1\right)\left(b+1\right)}+\frac{b^3}{\left(b+1\right)\left(c+1\right)}+\frac{c^3}{\left(c+1\right)\left(a+1\right)}\ge\frac{3}{4}\)
cho a,b,c là các số thực dương thỏa mãn \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1.\\ CMR:\left(a-1\right)\left(b-1\right)\left(c-1\right)\le\frac{1}{8}\left(a+1\right)\left(b+1\right)\left(c+1\right)\)
Cho a,b,c dương thõa mãn abc=1
CMR \(\frac{a}{\left(a+1\right)\left(b+1\right)}+\frac{b}{\left(b+1\right)\left(c+1\right)}+\frac{c}{\left(c+1\right)\left(a+1\right)}\ge\frac{3}{4}\)
Cho a,b,c dương thõa mãn abc=1
CMR \(\frac{a}{\left(a+1\right)\left(b+1\right)}+\frac{b}{\left(b+1\right)\left(c+1\right)}+\frac{c}{\left(c+1\right)\left(a+1\right)}\ge\frac{3}{4}\)
Cho a,b,c dương thõa mãn abc=1
CMR \(\frac{a}{\left(a+1\right)\left(b+1\right)}+\frac{b}{\left(b+1\right)\left(c+1\right)}+\frac{c}{\left(c+1\right)\left(a+1\right)}\ge\frac{3}{4}\)