Question

Tìm x, biết:

\(\dfrac{x+4}{10}=\dfrac{10}{x+4}\)

Answer 1

Đk \(x+4\ne0\Leftrightarrow x\ne-4\)

\(\dfrac{x+4}{10}=\dfrac{10}{x+4}\Leftrightarrow\left(x+4\right)^2=10^2\)

\(\Leftrightarrow\left|x+4\right|=10\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=10\\x+4=-10\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-14\end{matrix}\right.\)

Answer 2

\(\dfrac{x+4}{10}=\dfrac{10}{x+4}\)

\(=>x+4.x+4=10.10\)

=> \(\left(x+4\right)^2=10^2\) hoặc = \(\left(-10\right)^2\)

=> \(x+4=10\) hoặc \(x+4=\left(-10\right)\)

\(x=10-4\) \(x=\left(-10\right)-4\)

\(x=6\) \(x=\left(-14\right)\)

Vậy x = 6 hoặc x = -14