Question

Answer 1

a: Khi x=9 thì \(A=\dfrac{9+3}{\sqrt{9}-2}=12\)

b: \(B=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)+5\sqrt{x}-2}{x-4}\)

\(=\dfrac{x-3\sqrt{x}+2+5\sqrt{x}-2}{x-4}=\dfrac{x+2\sqrt{x}}{x-4}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)

c: P=A:B

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

\(P-2=\dfrac{x-2\sqrt{x}+3}{\sqrt{x}}=\dfrac{x-2\sqrt{x}+1+2}{\sqrt{x}}=\dfrac{\left(\sqrt{x}-1\right)^2+2}{\sqrt{x}}>0\)

=>P>2