Question

Bài 2 : Cho \(A=\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}}+\frac{1-\sqrt{x}}{x+\sqrt{x}}\right)\)

a, Rút gọn A

b, Tìm A khi x = 9

c, Tìm các giá trị của x thỏa mãn : \(\sqrt{x}\times A=6\sqrt{x}+3\)

Answer 1

\(ĐK:x>0\)

\(A=\frac{x-1}{\sqrt{x}}:\left(\frac{x-1}{x+\sqrt{x}}+\frac{1-\sqrt{x}}{x+\sqrt{x}}\right)=\frac{x-1}{\sqrt{x}}:\frac{x-\sqrt{x}}{x+\sqrt{x}}=\frac{\sqrt{x}\left(x-1\right)\left(\sqrt{x}+1\right)}{x\left(\sqrt{x}+1\right)}=\frac{x-1}{\sqrt{x}}\)

\(b,x=9\Rightarrow A=\frac{8}{3}\)

\(\sqrt{x}\times A=6\sqrt{x}+3\Leftrightarrow x-1=6\sqrt{x}+3\left(\sqrt{x}-3\right)^2=13\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}-3=-\sqrt{13}\\\sqrt{x}-3=\sqrt{13}\end{matrix}\right.\Leftrightarrow\sqrt{x}-3=\sqrt{13}\left(vì:-\sqrt{13}+3< 0\right)\Leftrightarrow\sqrt{x}=\sqrt{13}+3\Leftrightarrow x=22+2\sqrt{117}\)