Giải phương trình

\(\sqrt{x+1}\) + \(\sqrt{4-x}\) + \(\sqrt{\left(x+1\right)\left(4-x\right)}\) =5

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

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

\(\sqrt{x+\sqrt{6x-9}}\) + \(\sqrt{x-\sqrt{6x-9}}\) = \(\sqrt{6}\)

\(\sqrt{x+2-4\sqrt{x-2}}\) +\(\sqrt{x-7-6\sqrt{x-2}}\) =1

\(\sqrt{x+4-4\sqrt{x}}\) +\(\sqrt{x+9-6\sqrt{x}}\) =1

Tìm GTLN

A= \(\sqrt{x-5}\) + 2\(\sqrt{1-9x}\)

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

C= 3x + 4\(\sqrt{1-x^2}\)

Cho a,b,c>0 t/m: ab+bc+ca=3

CMR: \(\dfrac{1}{a^2+b^2+1}\)+\(\dfrac{1}{b^2+c^2+1}\)+\(\dfrac{1}{c^2+a^2+1}\)<=1

Chõ,y,z>0 t/m ; x\(^2\)+y\(^2\)+z\(^2\)=3

CMR: \(\dfrac{1}{1+xy}\)+\(\dfrac{1}{1+yz}\)+\(\dfrac{1}{1+zx}\)>=\(\dfrac{3}{2}\)

Cho 2x+3y=1. Tìm GTLN

A= \(\sqrt{x-1}\)+\(\sqrt{y+1}\)