Question

Tìm x : \(2x-\sqrt{x}-15=0\)

Answer 1

Đk: \(x\ge0\)

\(2x-\sqrt{x}-15=0\)

\(2\left(x-\dfrac{\sqrt{x}}{2}+\dfrac{1}{16}\right)-\dfrac{121}{8}=0\)

\(2\left(\sqrt{x}-\dfrac{1}{4}\right)^2=\dfrac{121}{8}\)

\(\left(\sqrt{x}-\dfrac{1}{4}\right)^2=\dfrac{121}{16}\)

\(\left[{}\begin{matrix}\sqrt{x}-\dfrac{1}{4}=\dfrac{11}{4}\\\sqrt{x}-\dfrac{1}{4}=-\dfrac{11}{4}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=3\left(TM\right)\\\sqrt{x}=-\dfrac{5}{2}\left(L\right)\end{matrix}\right.\)\(\Rightarrow x=9\)