Question

Tìm x biết :

a) \(\frac{2x-1}{9}=\frac{25}{2x-1}\)

b) \(\frac{x+1}{x+3}=\frac{x+2}{x+5}\)

Cần nhất câu b) thôi nha!

Answer 1

b) \(\frac{x+1}{x+3}=\frac{x+2}{x+5}\)

\(\Rightarrow\left(x+1\right)\left(x+5\right)=\left(x+3\right)\left(x+2\right)\)

\(\Rightarrow x^2+x+5x+5=x^2+3x+2x+6\)

\(\Rightarrow6x=5x+1\)

\(\Rightarrow x=1\)

Vậy x = 1

Answer 2

a) \(\frac{2x-1}{9}=\frac{25}{2x-1}\)

\(\Rightarrow\left(2x-1\right)^2=225\)

\(\Rightarrow\left(2x-1\right)^2=15^2\)

\(\Rightarrow\left[\begin{matrix}2x-1=15\\2x-1=-15\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}2x=16\\2x=-14\end{matrix}\right.\)

\(\Rightarrow\left[\begin{matrix}x=8\\x=-7\end{matrix}\right.\)

Vậy \(x\in\left\{8;-7\right\}\)