Question

Determina perechile de numere intregi (x,y) care verifica relatia (x-3)* (y+1) = 11
va rog repede 100 de puncte si coroana

Answer 1

Răspuns: $\pink{\large \bf S \big\{(x,y)\big\} \in \Big\{\big(14,0 \big);\big(4,10 \big)\Big\}}$

Explicație pas cu pas:

11 este număr prim nu se descompune in alte numere, așadar îl putem scrie de 11 = 11 · 1

$\large \bf (x-3)\cdot(y+1) = 11 \cdot 1$

$\large \bf (x-3)\cdot(y+1) = 11 \implies$

• $\text{\bf Caz 1}$

$\large \bf x-3 = 1 \implies x=1+3\implies \boxed{\bf x = 4~\in \mathbb{Z}}$

$\large \bf y+1 = 11 \implies y=11-1\implies \boxed{\bf y = 10~\in \mathbb{Z}}$

• $\text{\bf Caz 2}$

$\large \bf x-3 = 11 \implies x=11+3\implies \boxed{\bf x = 14~\in \mathbb{Z}}$

$\large \bf y+1 = 1 \implies y=1-1\implies \boxed{\bf y = 0~\in \mathbb{Z}}$

$\pink{\large \bf S \big\{(x,y)\big\} \in \Big\{\big(14,0 \big);\big(4,10 \big)\Big\}}$

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