Question

Answer 1

a: \(A=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{x+\sqrt{x}+1}-\dfrac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}+2\left(\sqrt{x}+1\right)\)

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

b: \(\dfrac{x}{12}=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}{\sqrt{5}+3-\sqrt{5}}=\dfrac{1}{3}\)

=>x=36

Khi x=36 thì A=36+2=38

c: \(B=\dfrac{2\sqrt{x}}{x+2}\)

\(B-2=\dfrac{2\sqrt{x}-x-2}{x+2}=\dfrac{-\left(x-2\sqrt{x}+2\right)}{x+2}=\dfrac{-\left(x-2\sqrt{x}+1\right)-1}{x+2}=\dfrac{-\left(\sqrt{x}-1\right)^2-1}{x+2}< 0\)

=>B<2

căn x>0

x+2>0

=>B>0

=>0<B<2