Các câu hỏi tương tự
cho a,b,c>0.CMR
\(\dfrac{a+b}{ab+c^2}+\dfrac{b+c}{bc+a^2}+\dfrac{c+a}{ca+b^2}\le\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)
Cho a, b, c > 0 thỏa mãn \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\). CMR:
\(\dfrac{a^2}{a+bc}+\dfrac{b^2}{b+ac}+\dfrac{c^2}{c+ab}\ge\dfrac{a+b+c}{4}\)
23 tháng 6 2021 lúc 18:06
\(Cho a,b,c>0. Cmr: \dfrac{a^3b}{1+ab^2}+\dfrac{b^3c}{1+bc^2}+\dfrac{c^3a}{1+ca^2}>\dfrac{abc(a+b+c)}{1+abc}\)
Cho a, b, c > 0 và \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3\) . Tìm MAX của :
A= \(\dfrac{1}{\sqrt{a^2-ab+b^2}}+\dfrac{1}{\sqrt{b^2-bc+c^2}}+\dfrac{1}{\sqrt{c^2-ac+a^2}}\)
Cho a,b,c>0 thỏa mãn ab+bc+ca=1. CMR:
\(\left(\dfrac{a}{\sqrt{a^2+1}}+\dfrac{b}{\sqrt{b^2+1}}+\dfrac{c}{\sqrt{c^2+1}}\right)^3\le\dfrac{3}{2}\left(\dfrac{1}{a^2+1}+\dfrac{1}{b^2+1}+\dfrac{1}{c^2+1}\right)\)
cho a,b,c>0 thỏa mãn \(a^2+b^2+c^2=1\).CMR
\(\dfrac{\sqrt{ab+2c^2}}{\sqrt{1+ab-c^2}}+\dfrac{\sqrt{bc+2a^2}}{\sqrt{1+bc-a^2}}+\dfrac{\sqrt{ca+2b^2}}{\sqrt{1+ca-b^2}}\ge2+ab+bc+ca\)
8 tháng 4 2022 lúc 16:04
Cho a ; b ; c > 0 ; ab + bc + ac = 1
Tìm max : \(\dfrac{a}{a^2+1}+\dfrac{b}{b^2+1}-\dfrac{1}{c^2+1}\)
Cho a,b,c>0 thỏa mãn ab+bc+ac<=1
CMR: \(\dfrac{a}{\sqrt{a^2+1}}+\dfrac{b}{\sqrt{b^2+1}}+\dfrac{c}{\sqrt{c^2+1}}\le\dfrac{3}{2}\)
cho a,b,c>0;\(a+b+c,abc=1\).CMR
\(\dfrac{bc}{a^2\left(b+c\right)}+\dfrac{ca}{b^2\left(c+a\right)}+\dfrac{ab}{c^2\left(a+b\right)}\ge\dfrac{3}{2}\)