Riješimo jednadžbu: \[ ||x| - 2| = 1 \] **Korak 1: Uvođenje pomoćne varijable** Postavimo $$ y = |x| $$. Tada jednadžba postaje: \[ |y - 2| = 1 \] **Korak 2: Rješavanje jednadžbe s apsolutnom vrijednošću** Apsolutnu vrijednost možemo rastaviti na dva slučaja: 1. $$ y - 2 = 1 $$ 2. $$ y - 2 = -1 $$ **Rješenje prvog slučaja:** \[ y - 2 = 1 \] \[ y = 3 \] **Rješenje drugog slučaja:** \[ y - 2 = -1 \] \[ y = 1 \] **Korak 3: Vraćanje na varijablu $$ x $$** Podsjetimo se da je $$ y = |x| $$, dakle: 1. Kada je $$ y = 3 $$: \[ |x| = 3 \] \[ x = 3 \quad \text{ili} \quad x = -3 \] 2. Kada je $$ y = 1 $$: \[ |x| = 1 \] \[ x = 1 \quad \text{ili} \quad x = -1 \] **Konačno rješenje:** \[ x = -3, \, -1, \, 1, \, 3 \] Rješenja su $$ x = -3, \, -1, \, 1, \, 3 $$.

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3) $ ||x|-2|=1 $

Ask by Owen Gibson. in Serbia

Feb 04,2025

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Rješenja su $ x = -3, \, -1, \, 1, \, 3 $.

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To solve the equation $ ||x|-2|=1 $, we first recognize that the absolute value creates two scenarios. We start with the inner absolute value, breaking it down into two separate cases: 1. **Case 1**: $ |x| - 2 = 1 $ - This leads to $ |x| = 3 $. - Thus, $ x = 3 $ or $ x = -3 $. 2. **Case 2**: $ |x| - 2 = -1 $ - This simplifies to $ |x| = 1 $. - Therefore, $ x = 1 $ or $ x = -1 $. Combining both cases gives us the solutions: $ x = 3, -3, 1, -1 $. So the final solutions are $ x = 3, -3, 1, -1 $.

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3) \( ||x|-2|=1 \)

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