Tính \(A=\frac{1+\sqrt{11}}{2+\sqrt{11}}+\sqrt{\frac{2}{18-5\sqrt{11}}}\)

Cho \(a,b,c,d>0\) . Chm:

\(\frac{a}{b+c}+\frac{b}{c+d}+\frac{c}{d+a}+\frac{d}{a+b}\ge2\)

Cho \(a,b,c>0\) . Chm:

\(a^3+b^3+abc\ge ab\left(a+b+c\right)\)

Tìm GTLN của:

\(A=xyz\left(x+y\right)\left(y+z\right)\left(z+x\right)\) với x, y, z\(\ge\) 0; \(x+y+z=1\)

Cho \(a^3+b^3=2\) . Chmr: \(a+b\le2\)

Chm bđt:

\(\left(a_1+a_2+...+a_n\right)^2\le n\left(a_1^2+a_2^2+...+a_n^2\right)\)