Question

Answer 1

a,\(ĐK:x\ge0,x\ne4\)

b,\(P=\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)-4\left(\sqrt{x}-2\right)-8}{x-4}=\dfrac{x+2\sqrt{x}-4\sqrt{x}+8-8}{x-4}=\dfrac{x-2\sqrt{x}}{x-4}=\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{x-4}=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)

c,P nguyên \(< =.>\dfrac{\sqrt{x}}{\sqrt{x}+2}=1+\dfrac{-2}{\sqrt{x}+2}=1+\dfrac{-2}{\sqrt{x}+2}\) nguyên

\(< =>\sqrt{x}+2\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}=>x\in\left\{0;\right\}\left(tm\right)\)

d,\(=>\dfrac{\sqrt{x}}{\sqrt{x}+2}=\dfrac{1}{3}=>3\sqrt{x}=\sqrt{x}+2< =>2\sqrt{x}-2=0< =>x=1\left(tm\right)\)