Question

Tìm x:

\(\frac{x+2}{5}=\frac{1}{x-2}\)

Answer 1

\(\frac{x+2}{5}=\frac{1}{x-2}\)

\(\Leftrightarrow\left(x+2\right).\left(x-2\right)=5\)

\(\Leftrightarrow x.\left(x-2\right)+2.\left(x-2\right)=5\)

\(\Leftrightarrow x^2-2x+2x-4=5\)

\(\Leftrightarrow x^2=5+4\)

\(\Leftrightarrow x^2=9=3^2=\left(-3\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)

Vậy : \(x\in\left\{3,-3\right\}\)

Answer 2

\(\frac{x+2}{5}=\frac{1}{x-2}\)

=> \(\left(x+2\right).\left(x-2\right)=1.5\)

=> \(\left(x+2\right).\left(x-2\right)=5\)

=> \(x^2-2x+2x-4=5\)

=> \(x^2=5+4\)

=> \(x^2=9\)

=> \(\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)

Vậy \(x\in\left\{3;-3\right\}.\)

Chúc bạn học tốt!

Answer 3

Tìm x:

=> x^2-2^2=5

=> x^2=1

=> x=\(\sqrt{1}\)