Question

VA ROG URGENT DAU COROANA
FARA RĂSPUNSURI AIUREA VA ROG ​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$21 \ \ \vdots \ (2x+1) \implies (2x+1) \in \mathcal{D}_{21} \\ \implies (2x+1) \in \{1;3;7;21\} \Big| - 1$

$2x \in \{0;2;6;20\} \Big|:2 \implies x \in \{0;1;3;10\}$

$x \neq 0 \implies M = \{1;3;10\}$

$card \ M = 2^{3} = 8 \implies M \ are \ 8 \ submultimi$

∅; {1}; {3}; {10}; {1;3}; {1;10}; {3;10}; {1;3;10}

b)

$\dfrac{3y+5}{2y-4} = \dfrac{3y+5}{2(y-2)} \in \mathbb{N}$

dacă (2y - 4) divide (3y + 5), atunci (2y - 4) divide și 2×(3y + 5)

$\dfrac{2(3y+5)}{2(y-2)} = \dfrac{3y+5}{y-2} = \dfrac{3y - 6 + 11}{y-2} = \dfrac{3(y-2)+11}{y-2} = 3 + \dfrac{11}{y-2} \in \mathbb{N} \implies \dfrac{11}{y-2} \in \mathbb{N} \iff (y-2) \in \mathcal{D}_{11} \implies (y-2) \in \{1;11\} \ \Big|+2 \iff y \in \{3;13\} \implies N = \{3;13\}$

$\implies \bf M \cap N = \{3\}$