cho a,b,c > 0 .Cmr:
\(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge\sqrt{a^2-ab+b^2}+\sqrt{b^2-bc+c^2}+\sqrt{c^2-ca+a^2}\)
Cho a, b, c > 0
Cmr: \(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge\sqrt{a^2-ab+b^2}+\sqrt{b^2-bc+c^2}+\sqrt{c^2-ca+a^2}\)
Cho 3 số thực dương a,b,c. CMR \(\frac{a^2}{\sqrt{3a^2+8b^2+14ab}}+\frac{b^2}{\sqrt{3b^2+8c^2+14bc}}+\frac{c^2}{\sqrt{3c^2+8a^2+14ac}}\ge\frac{1}{5}\left(a+b+c\right)\)
cho a,b,c là số thực dương thỏa mãn \(abc\le1\)
CMR:
\(\frac{a^3+1}{b\sqrt{a^2+1}}+\frac{b^3+1}{c\sqrt{b^2+1}}+\frac{c^3+1}{a\sqrt{c^2+1}}\ge\sqrt{2}\left(a+b+c\right)\)
cho a,b,c > 0 thỏa mãn ab+bc+ca=1. Cmr:
\(a+b+c+\frac{ab}{b+c}+\frac{bc}{c+a}+\frac{ca}{a+b}\ge\frac{3\sqrt{3}}{2}\)
1:Cho x;y>0:\(\frac{2}{x}+\frac{3}{y}=6\).Tìm min P=x+y
2:Cho x;y;z>0:x+y+z\(\le\)1.Chứng minh\(\sqrt{x^2+\frac{1}{x^2}}+\sqrt{y^2+\frac{1}{y^2}}+\sqrt{z^2+\frac{1}{z^2}}\ge\sqrt{82}\)
3:cho a;b;c;d>0.Chứng minh\(\frac{a^2}{b^5}+\frac{b^2}{c^5}+\frac{c^2}{d^5}+\frac{d^2}{a^5}\ge\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}+\frac{1}{d^3}\)
4:Tìm max,min y=x+\(\sqrt{4-x^2}\)
5:Cho \(a\ge1;b\ge1\).Chứng minh \(a\sqrt{b-1}+b\sqrt{a-1}\le ab\)
6:Chứng minh:\(\left(ab+bc+ca\right)^2\ge3\text{a}bc\left(a+b+c\right)\)
cho a,b,c là độ dài 3 cạnh của tam giác. CMR:
\(\frac{\sqrt{a}}{b+c-a}+\frac{\sqrt{b}}{a+c-b}+\frac{\sqrt[]{c}}{a+b-c}\ge\frac{a+b+c}{\sqrt{abc}}\)
Cho a,b,c>0 thỏa mãn ab+bc+ac=1. CMR \(\frac{a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\le\frac{3}{2}\)
Cho a,b,c > 0. Chứng minh:
\(\frac{a}{\sqrt[3]{4\left(b^3+c^3\right)}}+\frac{b}{c+a}+\frac{c}{a+b}\ge\frac{3}{2}\)
