Question

Se considera multimea A={x apartine Z|x+6/x-1 apartine Z}. Suma elementelor multimii A este:
As dori mod de rezolvare dacă se poate,nu doar rezultat.
Variantele sunt A. 4,B. 2,C. 0si D. -2​.

Answer 1

x-1 | x+6

x-1 | x-1

Le scadem

x-1 | 7

x-1={7,-7,1,-1}

x={8, -6, 2, 0}

Suma elementelor=8-6+2+0=4

Raspuns: A) 4

Answer 2

Răspuns: Varianta corectă → d)

Explicație:

$\bf x - 1 ~~\big|~~ x + 6$

$\bf \underline{x - 1 ~~\big|~~ x -1~~~~~~~}~_{\bf (-)}$

$\bf x-1~~\big |~~ 7\implies x-1 \in D_{7}$

$\bf x-1 \in \{-7;-1;1;7\}~~~\bigg|_{+1}$

$\bf x \in \{-6;0;2;8\}$

Suma elementelor A = -6 + 0 + 2 + 8

Suma elementelor A = 4

Varianta corectă → d)