Question

Determinoti toate nr intregi x care
verifica etopa Ix2 - 1|<4​

Answer 1

Răspuns:

$S = \{-2, -1, 0, 1, 2\}$

Explicație pas cu pas:

$|x^2 - 1| < 4\\\implies -4 < x^2 - 1 < 4\Big | + 1\\-3 < x^2 < 5\\\textrm{Pentru prima inecutatie:}\\x^2 > 0 \Rightarrow x^2 > -3, \forall x \in \mathbb{R}\\\textrm{Pentru a doua inecutatie:}\\x^2 < 5\Rightarrow x \in (-\sqrt{5}, \sqrt{5})\\ \sqrt{5} \approx 2.2\Rightarrow x \in (-2.2, 2.2).\\\textrm{Deoarece } x \in \mathbb{Z}\textrm{ trebuie sa intersectam multimile:}\\S = (-2.2, 2.2) \cap \mathbb{Z} = \{-2, -1, 0, 1, 2\}$