Răspuns:
Explicație pas cu pas:
5(x-1)/9=80/x-1 (x-1)²=80×9/5 (x-1)²=2³×3²×x2 x-1=12
x=11
[tex]\it \dfrac{5x-5}{9}=\dfrac{80}{x-1} \Rightarrow \dfrac{5(x-1)}{9}=\dfrac{80}{x-1} \Rightarrow 5(x-1)^2=80\cdot9|_{:5} \Rightarrow \\ \\ \Rightarrow (x-1)^2=16\cdot9 \Rightarrow\sqrt{(x-1)^2}=\sqrt{16\cdot9} \Rightarrow |x-1| = 4\cdot3 \Rightarrow\\ \\ \Rightarrow x+1=\pm12\Rightarrow x-1\in\{-12,\ 12\}|_{+1} \Rightarrow x\in\{-11,\ 13\}[/tex]
