18 tháng 9 2022 lúc 21:57
Các câu hỏi tương tự
Cho a, b, c > 0 . CMR :
A= \(\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{a+c}}+\sqrt{\dfrac{c}{a+b}}>2\)
12 tháng 9 2021 lúc 9:01
Cho a,b∈Z, c≠0 và \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\)
CMR: \(\sqrt{a+b}=\sqrt{a+c}+\sqrt{b+c}\)
Cho a, b, c > 0. CMR :
\(\dfrac{\sqrt{a^2+b^2}}{c}+\dfrac{\sqrt{b^2+c^2}}{a}+\dfrac{\sqrt{a^2+c^2}}{b}\ge2\left(\dfrac{a}{\sqrt{b^2+c^2}}+\dfrac{b}{\sqrt{a^2+c^2}}+\dfrac{c}{\sqrt{a^2+b^2}}\right)\)
Cho a,b,c>0.CMR \(\sqrt{1+\dfrac{16a}{b+c}}+\sqrt{1+\dfrac{16b}{a+c}}+\sqrt{1+\dfrac{16c}{a+b}}\ge9\)
CMR: \(\dfrac{a^2}{b}+\dfrac{b^2}{c}+\dfrac{c^2}{a}>=\sqrt{\dfrac{a^2+b^2}{2}}+\sqrt{\dfrac{b^2+c^2}{2}}+\sqrt{\dfrac{c^2+a^2}{2}}\left(a,b,c>0\right)\)
Cho \(a,b,c>0\). Chứng minh:
\(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}\)
cho a,b,c>0 cm \(\dfrac{a+b}{\sqrt{c}}\) +\(\dfrac{b+c}{\sqrt{a}}\) +\(\dfrac{c+a}{\sqrt{b}}\)≥2(\(\sqrt{a}+\sqrt{b}+\sqrt{c}\))
Cho 3 số thực dương a,b.c thỏa mãn abc=1 cmr:\(\dfrac{b+c}{\sqrt{a}}+\dfrac{c+a}{\sqrt{b}}+\dfrac{a+b}{\sqrt{c}}\ge\sqrt{a}+\sqrt{b}+\sqrt{c}+3\)
Cho các số thực dương a+b+c=\(\sqrt{a}+\sqrt{b}+\sqrt{c}=2\\\).CMR
\(\dfrac{\sqrt{a}}{1+a}+\dfrac{\sqrt{b}}{1+b}+\dfrac{\sqrt{c}}{1+c}=\dfrac{2}{\sqrt{\left(1+a\right)\left(1+b\right)\left(1+c\right)}}\)
Cho a,b,c>0 thỏa mãn ab+bc+ca=1. CMR:
\(\left(\dfrac{a}{\sqrt{a^2+1}}+\dfrac{b}{\sqrt{b^2+1}}+\dfrac{c}{\sqrt{c^2+1}}\right)^3\le\dfrac{3}{2}\left(\dfrac{1}{a^2+1}+\dfrac{1}{b^2+1}+\dfrac{1}{c^2+1}\right)\)