Question

giúp mình nhanh ạ

Answer 1

Bài 17:

a: Ta có: \(Q=\dfrac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}-\dfrac{\sqrt{x}+1}{\sqrt{x}+2}+\dfrac{\sqrt{x}-2}{1-\sqrt{x}}\)

\(=\dfrac{3x+3\sqrt{x}-3-x+1-x+4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}\)

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

\(=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)

b: Thay \(x=4+2\sqrt{3}\) vào Q, ta được:

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

c: Để Q=3 thì \(\sqrt{x}+1=3\sqrt{x}-3\)

\(\Leftrightarrow-2\sqrt{x}=-4\)

\(\Leftrightarrow\sqrt{x}=2\)

hay x=4