Question

Determinați mulțimea A={ x aparține Z | √(4x-5)/√(x+1 aparține N) .​

Answer 1

Explicație pas cu pas:

$\dfrac{4x - 5}{x + 1} \geqslant 0$

$\implies x \in \Big(-\infty ; -1 \Big) \cup \Big[\dfrac{5}{4} ; +\infty \Big)$

$\sqrt{\dfrac{4x - 5}{x + 1}} \in \mathbb{N} \implies \dfrac{4x - 5}{x + 1} \in \mathbb{N}$

$\dfrac{4x - 5}{x + 1} = \dfrac{4(x + 1) - 9}{x + 1} = 4 - \dfrac{9}{x + 1}$

$\implies (x + 1) \in \mathcal{D}_{ \pm9 } \iff (x + 1) \in \Big\{- 9; - 3; - 1; 1; 3; 9\Big\}$

$\iff x \in \Big\{- 10; - 4; - 2; 0; 2; 8\Big\}$

se verifică => x = 2

=> A = {2}