Question

Tìm x:

\(\dfrac{x+\dfrac{1}{2}}{4}=\dfrac{25}{x+\dfrac{1}{2}}\)

Answer 1

\(\dfrac{x+\dfrac{1}{2}}{4}=\dfrac{25}{x+\dfrac{1}{2}}\left(x\ne-\dfrac{1}{2}\right)\)

\(\Rightarrow\left(x+\dfrac{1}{2}\right)^2=4.25=100\)

\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{2}=10\\x+\dfrac{1}{2}=-10\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=10-\dfrac{1}{2}=\dfrac{19}{2}\\x=-10-\dfrac{1}{2}=-\dfrac{21}{2}\end{matrix}\right.\)

Vậy \(x\in\left\{-\dfrac{21}{2};\dfrac{19}{2}\right\}\)