Question

Сумма корней уравнения ||x – 4| – 12| = 3

Answer 1

корни уравнения равны 19 и -19

значит сумма корней будет равна 0

Answer 2

To find the sum of the roots of the equation ||x – 4| – 12| = 3, we first need to solve the equation.

Let's break it down step by step:

1. First, let's handle the inner absolute value: |x - 4| = 3 + 12 |x - 4| = 15

2. Now, we have two cases to consider since the absolute value of a number can be positive or negative: Case 1: x - 4 = 15 Case 2: -(x - 4) = 15

3. Solving each case separately:

   Case 1: x - 4 = 15 x = 15 + 4 x = 19

   Case 2: -(x - 4) = 15 -x + 4 = 15 -x = 15 - 4 -x = 11 x = -11

So, we have two potential solutions: x = 19 and x = -11.

Now, let's calculate the sum of these roots: Sum of roots = 19 + (-11) = 8

Therefore, the sum of the roots of the equation ||x – 4| – 12| = 3 is 8.