CMR:\(\frac{a}{\sqrt{b}}-\sqrt{a}\ge\sqrt{b}-\frac{b}{\sqrt{a}}\)

Cho \(\sqrt{x}+2\sqrt{y}=10\) CMR x+y\(\ge\)0

cho x,y,z tm \(\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}=2\)

CMR xyz=\(\frac{1}{8}\)

cho B=\(\frac{x^3}{1+y}+\frac{y^3}{1+x}\) (x>0,y>0) tm xy=1

cmr B\(\ge1\)

a,b,c là 3 cạnh tam giác tm \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}\)

cmr \(\frac{1}{a^{2019}}+\frac{1}{b^{2019}}+\frac{1}{c^{2019}}=\frac{1}{a^{2019}+b^{2019}+c^{2019}}\)

\(\frac{bc}{a}+\frac{ac}{b}+\frac{ab}{c}\ge\sqrt{3\left(a^2+b^2+c^2\right)}\)(a,b,c>0)

cmr

\(\frac{\left(a+b\right)^2}{2}+\frac{a+b}{4}\ge a\sqrt{a}+b\sqrt{b}\)

\(\frac{\sqrt{a}}{b+c}+\frac{\sqrt{b}}{c+a}+\frac{\sqrt{c}}{a+b}>2\left(a,b,c>0\right)\)

cmr\(\frac{\left(a+b\right)^2}{2}+\frac{a+b}{4}\ge a\sqrt{b}+b\sqrt{a}\left(a,b>0\right)\)