Question

ma puteți ajuta ,va rog frumos​

Answer 1

$\it Determina\c{\it t}i\ a\in\mathbb{R},\ dac\breve a\ A=B,\ unde:\\ \\ A=\{x\in\mathbb{R}\Big|\ 5(x+2)-2(1-x)=x+20}\}\\ \\ B=\{x\in\mathbb{R}\Big|\ (a+2)x-a=1\}\\ \\ \\ \underline{Rezolvare:}\\ \\5(x+2)-2(1-x)=x+20 \Rightarrow 5x+10-2+2x=x+20 \Rightarrow \\ \\ \Rightarrow 7x+8=x+20 \Rightarrow 7x-x=20-8 \Rightarrow 6x=12|_{:6} \Rightarrow x=2 \Rightarrow A=\{2\}\\ \\ (a+2)x-a=1 \Rightarrow (a+2)x=a+1 \Rightarrow x=\dfrac{a+1}{a+2} \Rightarrow B=\Big\{\dfrac{a+1}{a+2},\ a\in\mathbb{R}\Big\}$

$\it A=B \Rightarrow \dfrac{a+1}{a+2}=2 \Rightarrow a+1=2a+4 \Rightarrow 1-4=2a-a \Rightarrow a=-3$