Question

fie A={x apartine Z\ 6 supra 2x-1 apartine la Z}. Calculati A ∩ [-1;0]

Answer 1

Răspuns:

Explicație pas cu pas:

6/2x-1

2x - 1 = 1 deci x = 1

2x - 1 = -1 deci x = 0

2x - 1 = 2 deci x = 1/2, nu apartine lui Z

2x - 1 = -2 deci x = -1/2, nu apartine lui Z

2x - 1 = 3 deci x = 2

2x - 1 = -3 deci x = -1

2x - 1 = 6 deci x = 7/2, nu apartine lui Z

2x - 1 = -6 deci x = -5/2 nu apartine lui Z

A = {-1; 0; 1; 2}

A ∩ [-1;0] = {-1; 0}

Answer 2

$\it \dfrac{6}{2x-1}\in\mathbb{Z}\Rightarrow 2x-1|6 \Rightarrow 2x-1\in D_6 \Rightarrow 2x-1\in\{\pm1,\ \pm2,\ \pm3,\ \pm6\}\Rightarrow \\ \\ \\ \Rightarrow 2x-1\in\{-6,\ -3,\ -2,\ -1,\ 1,\ 2,\ 3,\ 6\}|_{+1}\Rightarrow\\ \\ \\ \Rightarrow 2x\in\{-5,\ -2,\ -1,\ 0,\ 2,\ 3,\ 4,\ 7\}\ \ \ (*)$

$\it x\in\mathbb{Z} \stackrel{(*)}{\Longrightarrow} 2x\in\{-2,\ 0,\ 2,\ 4\}|_{:2} \Rightarrow x\in\{-1,\ 0,\ 1,\ 2\}\\ \\ \\ A=\{-1,\ 0,\ 1,\ 2\}\\ \\ \\ A\cap [-1,\ 0]=\{-1,\ 0\}$