Cho a,b,c > 0 thỏa mãn a+b+c=1 CMR \(\dfrac{a}{\sqrt{2a+b}}+\dfrac{b}{\sqrt{2b+c}}+\dfrac{c}{\sqrt{2c+a}}\le1\)

CMR \(cos36^o=\dfrac{\sqrt{5}+1}{4}\)

Cho a,b,c>0 thỏa mãn a+b+c=1 CMR \(\dfrac{a}{\sqrt{a+bc}}+\dfrac{b}{\sqrt{b+ca}}+\dfrac{c}{\sqrt{c+ab}}\le\dfrac{3}{2}\)

Cho a,b,c>0 thỏa mãn \(a+b+c\le3\)CMR \(\dfrac{6}{a}+\dfrac{3}{b^2}+\dfrac{2}{c^3}\ge11\)

CMR với a,b,c >0 \(\dfrac{a^3}{a^2+b^2}+\dfrac{b^3}{b^2+c^2}+\dfrac{c^3}{c^2+a^2}\ge\dfrac{a+b+c}{2}\)

Cho x,y,z \(\ge\)0 thỏa mãn \(x+y+z=\dfrac{3}{2}\).Tìm GTLN của \(A=x\sqrt[3]{y+z}+y\sqrt[3]{z+x}+z\sqrt[3]{x+y}\)