\(VT=\sum\dfrac{a}{a+b}< \sum\dfrac{a+c}{a+b+c}=2\)
\(VP=\sum\sqrt{\dfrac{a}{b+c}}=\sum\dfrac{a}{\sqrt{a}\cdot\sqrt{b+c}}>\sum\dfrac{2a}{a+b+c}=2\)
\(VP>2>VT\)
Cho a, b, c > 0. Chứng minh \(\sqrt{\dfrac{a^3}{b^3}}+\sqrt{\dfrac{b^3}{c^3}}+\sqrt{\dfrac{c^3}{a^3}}\ge\dfrac{a}{b}+\dfrac{b}{c}+\dfrac{c}{a}\)
cho 3 số thực dương a,b,c thỏa mãn \(\dfrac{a}{1+a}+\dfrac{b}{1+b}+\dfrac{c}{1+c}=2\) .Chứng minh:
\(\dfrac{\sqrt{a}+\sqrt{b}+\sqrt{c}}{2}\ge\dfrac{1}{\sqrt{a}}+\dfrac{1}{\sqrt{b}}+\dfrac{1}{\sqrt{c}}\)
Cho a,b,c > 0 . CMR :
\(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}\)
Cho a, b, c > 0. Chứng minh rằng: \(\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}>2\)
Cho a, b, c>0. CMR: \(\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}>2\)
Cho a,b,c>0 tm a+b+c=5. \(\sqrt{a}+\sqrt{b}+\sqrt{c}=3\).
C/m\(\dfrac{\sqrt{a}}{2+a}+\dfrac{\sqrt{b}}{2+b}+\dfrac{\sqrt{c}}{2+c}=\dfrac{4}{\sqrt{\left(a+2\right)\left(b+2\right)\left(c+2\right)}}\)
cho a,b,c >0
chứng minh rằng
\(\dfrac{a^2}{\sqrt{b^2+c^2}}+\dfrac{b^2}{\sqrt{a^2+c^2}}+\dfrac{c^2}{\sqrt{a^2+b^2}}\ge\dfrac{a+b+c}{\sqrt{2}}\)
Cho a, b, c > 0 thoả mãn: \(a+b+c=\sqrt{a}+\sqrt{b}+\sqrt{c}=2\). Chứng minh rằng: \(\dfrac{\sqrt{a}}{a+1}+\dfrac{\sqrt{b}}{b+1}+\dfrac{\sqrt{c}}{c+1}=\dfrac{2}{\sqrt{\left(a+1\right)\left(b+1\right)\left(c+1\right)}}\)
cho a,b dương và c ≠ 0 thỏa mãn \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\). CMR: \(\sqrt{a+b}=\sqrt{b+c}+\sqrt{c+a}\)
