Question

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$| {x}^{2} - 1| = 3$

Answer 1

|x²-1|=3 <=> 3 <= x²-1 < 4 => 3 <= x²-1 <=> 4 <=x² dar deoarece x∈R => (-∞,-2] ∪ [2,∞) si x²-1 < 4 <=> x² < 5 dar deoarece x∈R => x∈(-√5,√5) . Se poate observa faptul ca √4 < √5 < √9 <=> 2 < √5 < 3 <=> -3 < -√5 < -2 .

Asadar x∈(-∞,-2] ∪ [2,∞) ∩ (-√5,√5) <=> x∈ (-√5,-2] ∪ [2,√5) .