Question

Aflati x apartine Z ,astfel incat 5/2-x apartine Z
Dau multe puncte!

Answer 1

$\frac{5}{2 - x} \: \in \: \mathbb{Z} = > (2 - x) \: \in \: D_{5}$

$D_{5}=\left \{ \pm1,\pm5 \right \}$

$1)2 - x = - 1$

$- x = - 1 - 2$

$- x = - 3 \: | \times ( - 1)$

$x = 3 \: \in \: \mathbb{Z}$

$\frac{5}{2 - 3} = \frac{5}{ - 1} = - 5 \: \in \: \mathbb{Z}$

$2)2 - x = 1$

$- x = 1 - 2$

$- x = - 1 \: | \times ( - 1)$

$x = 1 \: \in \: \mathbb{Z}$

$\frac{5}{2 - 1} = \frac{5}{1} = 5 \: \in \: \mathbb{Z}$

$3)2 - x = - 5$

$- x = - 5 - 2$

$- x = - 7 \: | \times ( - 1)$

$x = 7 \: \in \: \mathbb{Z}$

$\frac{5}{2 - 7} = \frac{5}{ - 5} = - 1 \: \in \: \mathbb{Z}$

$4) 2 - x = 5$

$- x = 5 - 2$

$- x = 3 \: | \times ( - 1)$

$x = - 3 \: \in \: \mathbb{Z}$

$\frac{5}{2 - ( - 3)} = \frac{5}{2 + 3} = \frac{5}{5} = 1 \: \in \: \mathbb{Z}$