\(vìa;b>0\Rightarrow\frac{a}{a+b}\frac{b}{b+c}\) (2)
.................................................\(\sqrt{\frac{c}{a+c}}>\frac{c}{c+a}\) (3)
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Cho a, b, c > 0
C/m: \(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}<\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}\)
cho a,b,c >0 chứng minh rằng \(\sqrt{\frac{a+b}{c}}+\sqrt{\frac{b+c}{a}}+\sqrt{\frac{c+a}{b}}>=2\left(\sqrt{\frac{c}{a+b}}+\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{a+c}}\right)\)
Cho a,b,c lớn hơn 0:
\(\sqrt{\frac{a+b}{c}}+\sqrt{\frac{b+c}{a}}+\sqrt{\frac{c+a}{b}}\ge2\left(\sqrt{\frac{c}{a+b}}+\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}\right)\)
cho a; b; c >0 chứng minh rằng \(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}>\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{a+c}}+\sqrt{\frac{c}{a+b}}\)
a) a,b,c > 0 .C/m: \(1<\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}<2\)
b) C/m: \(\frac{a}{a+b}+\frac{b}{B+c}+\frac{c}{c+a}<\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}\)
Cho a,b,c > 0 . Chứng minh rằng
\(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}< \sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}\)
Cho a,b,c>0 . chứng minh rằng:
\(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}< \sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}\)
cho a,b,c>0. Chứng minh rằng:
\(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}< \sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}\)
cho a,b,c>0 thoải mãn a+b+c=1 chứng minh\(\frac{a}{b}+\frac{b}{a}+\frac{b}{c}+\frac{c}{b}+\frac{a}{c}+\frac{c}{a}+6\)>=\(2\sqrt{2}.\left(\sqrt{\frac{1-a}{a}}+\sqrt{\frac{1-b}{b}}+\sqrt{\frac{1-c}{c}}\right)\)