Question

Giúp mk câu b với ạ

Answer 1

1: \(P=\left(\dfrac{\sqrt{x-2}\left(3-\sqrt{x-2}\right)}{9-x+2}+\dfrac{x+7}{11-x}\right):\left(\dfrac{3\sqrt{x-2}+1-\sqrt{x-2}+3}{\sqrt{x-2}\left(\sqrt{x-2}-3\right)}\right)\)

\(=\dfrac{3\sqrt{x-2}-x+2+x+7}{11-x}:\dfrac{2\sqrt{x-2}+4}{\sqrt{x-2}\left(\sqrt{x-2}-3\right)}\)

\(=\dfrac{3\sqrt{x-2}+9}{11-x}\cdot\dfrac{\sqrt{x-2}\left(\sqrt{x-2}-3\right)}{2\sqrt{x-2}+4}\)

\(=\dfrac{-3\left(\sqrt{x-2}+3\right)}{2\left(\sqrt{x-2}+2\right)}\cdot\dfrac{\sqrt{x-2}}{\sqrt{x-2}+3}\)

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

2: Đặt căn x-2=a(a>=0)

=>P=-3a/(2a+4)

P nguyên

=>-3a chia hết cho 2a+4

=>-6a chia hết cho 2a+4

=>-6a-12+12 chia hết cho 2a+4

=>2a+4 thuộc {1;-1;2;-2;3;-3;4;-4;6;-6;12;-12}

=>a thuộc {1;4}

=>x-2=1 hoặc x-2=16

=>x=3 hoặc x=18