BĐT sai với $(x,y,z)=(4,6,1)$
BĐ cũng sai với \(\left(x;y;z\right)=\left(1;5;3\right)\)
Cho x, y, z >0 thoả mãn \(x^2+y^2+z^2=1\) . Cmr: \(\frac{x+y+z}{xy+yz+xz}\ge\sqrt{3}+\frac{1}{2\sqrt{3}}\left[\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2\right]\)
cho x,y,z> 0 thỏa mãn \(x^3+y^3+z^3=1\)
Cmr: \(\frac{x^2}{\sqrt{1-x^2}}+\frac{y^2}{\sqrt{1-y^2}}+\frac{z^2}{\sqrt{1-z^2}}\ge2\)
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 3 số thực dương x, y, z thỏa mãn \(x^3+y^3+z^3=1\). CMR:
\(\frac{x^2}{\sqrt{1-x^2}}+\frac{y^2}{\sqrt{1-y^2}}+\frac{z^2}{\sqrt{1-z^2}}\ge2\)
Cho x,y,z.0, cmr:
\(\Sigma_{cyc}\frac{x}{y}\ge\sqrt{\frac{x^2+y^2+z^2}{xy+yz+zx}}\)tth
cho x,y,z > 0. Cmr:
\(\frac{x}{\sqrt{x^2-8yz}}+\frac{y}{\sqrt{y^2-8xz}}+\frac{z}{\sqrt{z^2-8xy}}\ge1\)
cho x, y, z > 0 . Cmr:
\(\frac{x}{\sqrt{x^2+8yz}}+\frac{y}{\sqrt{y^2+8xz}}+\frac{z}{\sqrt{z^2+8xy}}\ge1\)
cho x,y,z > 0. Cmr:
\(\frac{x}{\sqrt{x^2+8yz}}+\frac{y}{\sqrt{y^2+8xz}}+\frac{z}{\sqrt{z^2+8xy}}\ge1\)
Cho 3 số dương x,y,z có tổng bằng 1.CMR\(\sqrt{\frac{xy}{xy+z}}+\sqrt{\frac{yz}{yz+x}}+\sqrt{\frac{zx}{zx+y}}\le\frac{3}{2}\)
