\(\frac{1+\sqrt{1}+\sqrt{2}}{1-\sqrt{1}+\sqrt{2}}+...+\frac{1+\sqrt{99}+\sqrt{100}}{1-\sqrt{99}+\sqrt{100}}\)

a,b,c>0, biết a+b+c=3

CMR a)\(\frac{ab}{\sqrt{a^2+3b^2}}+\frac{bc}{\sqrt{b^2+3c^2}}+\frac{ac}{\sqrt{c^2+3a^2}}\)≤\(\frac{3}{2}\)

b)\(\frac{a}{\sqrt{b^2+3}}+\frac{b}{\sqrt{c^2+3}}+\frac{c}{\sqrt{a^2+3}}\)≥\(\frac{3}{2}\)

\(\frac{1-\sqrt{1}+\sqrt{2}}{1+\sqrt{1}+\sqrt{2}}+...+\frac{1-\sqrt{99}+\sqrt{100}}{1+\sqrt{99}+\sqrt{100}}\)

\(\left\{{}\begin{matrix}x^2=y+\frac{4}{y}\\y^2=x+\frac{4}{x}\end{matrix}\right.\)

\(x^2-8x+5=\sqrt{3x+1}\)

cho các số thực x,y thỏa mãn\(\left(x+\sqrt{1+y^2}\right)\left(y+\sqrt{1+x^2}\right)=1\)

c/m\(\left(x+\sqrt{1+x^2}\right)\left(y+\sqrt{1+y^2}\right)=1\)

\(\sqrt{4-3\sqrt{10-3x}}=x-2\)