Question

\(\dfrac{x-1}{\sqrt{x}}=6\)

Answer 1

ĐKXĐ: \(x>0\)

\(\dfrac{x-1}{\sqrt{x}}=6\\ \Leftrightarrow x-1=6\sqrt{x}\\ \Leftrightarrow x^2-2x+1=36x\left(x\ge1\right)\\ \Leftrightarrow x^2-38x+1=0\\ \Leftrightarrow\left(x^2-38x+361\right)-360=0\\ \Leftrightarrow\left(x-19\right)^2-\sqrt{360^2}=0\\ \Leftrightarrow\left(x-19-6\sqrt{10}\right)\left(x-19+6\sqrt{10}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=19+6\sqrt{10}\left(tm\right)\\x=19-6\sqrt{10}\left(ktm\right)\end{matrix}\right.\)