Question

1)(2x-3) (-x-3)=02)( |x|-1) (|-x|+2)=0

Answer 1

Ответ:

Пошаговое объяснение:

1)(2x-3) (-x-3)=0

2х₁ - 3 = 0

х₁ = 3/2 = 1,5

-х₂-3 = 0

х₂ = -3

2)( |x|-1) (|-x|+2)=0

Так как |-x| >=0, то |-x|+2 > 0

Следовательно

|x₁|-1 = 0

|x₁| = 1

х₁₁ = 1

х₁₂ = -1

Answer 2

To solve these equations, we need to find the values of 'x' that make each equation true. Let's solve them one by one:

1. (2x - 3)(-x - 3) = 0

To solve this equation, we set each factor to zero and solve for 'x':

Setting the first factor (2x - 3) to zero: 2x - 3 = 0 2x = 3 x = 3/2

Setting the second factor (-x - 3) to zero: -x - 3 = 0 -x = 3 x = -3

So, the solutions for the equation are x = 3/2 and x = -3.

2. (|x| - 1)(|-x| + 2) = 0

To solve this equation, we again set each factor to zero and solve for 'x':

Setting the first factor (|x| - 1) to zero: |x| - 1 = 0 |x| = 1

This gives us two cases to consider:

Case 1: |x| = 1 If |x| = 1, it means x can be either 1 or -1.

Setting the second factor (|-x| + 2) to zero: |-x| + 2 = 0 |-(-1)| + 2 = 0 |1| + 2 = 0 1 + 2 = 0 (This is not possible)

So, in Case 1, we only have one solution: x = -1.

Case 2: |x| = 1 If |x| = 1, it means x can be either 1 or -1.

Setting the second factor (|-x| + 2) to zero: |-(1)| + 2 = 0 |1| + 2 = 0 1 + 2 = 0 (This is not possible)

So, in Case 2, we only have one solution: x = 1.

Therefore, the solutions for the equation are x = -1 and x = 1.

To summarize:

1. The solutions for the equation (2x - 3)(-x - 3) = 0 are x = 3/2 and x = -3.
2. The solutions for the equation (|x| - 1)(|-x| + 2) = 0 are x = -1 and x = 1.