Question

1)(-3+х)*х=0 2)|х+1|*(|х|+1)=0 3)|-х-1|*(|х|-1)=0 4)-|-х|*(2-х)=0 5)(|х|+1)*(2-х)=0

Answer 1

Ответ:

1) х = 3 или х = 0; 2) х = - 1; 3) х = - 1 или х = 1; 4) х = 0 или х = 2; 5) х = 2.

Пошаговое объяснение:

1)(- 3 + х)*х = 0

х = 0

или

- 3 + х = 0

х = 0

или

х = 3

2)|х + 1|*(|х| + 1) = 0

|х + 1| = 0

или

|х| + 1 = 0

х = - 1

Второе равенство не имеет решения, потому что требуется отрицательный икс, а модуль не даст минусу появиться.

3)|- х - 1|*(|х| - 1) = 0

|- х - 1| = 0

или

|х| - 1 = 0

х = - 1

или

х = 1 и х = -1

4)-|-х|*(2 - х) = 0

х = 0

или

2 - х = 0

х = 0

или

х = 2

5)(|х| + 1)*(2 - х) = 0

|х| + 1 = 0

или

2 - х = 0

У первого равенства решения нет

х = 2

Answer 2

Let's solve each equation step by step:

1. (-3 + x) * x = 0

To find the solutions, we set each factor equal to zero and solve for x separately:

-3 + x = 0 => x = 3

x = 0

So the solutions for this equation are x = 3 and x = 0.

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

For the product to be zero, at least one of the factors must be zero. Let's consider both cases:

Case 1: |x + 1| = 0

If |x + 1| = 0, it means that x + 1 = 0. Solving for x, we have:

x + 1 = 0 => x = -1

Case 2: |x| + 1 = 0

If |x| + 1 = 0, it means that |x| = -1, which is not possible since the absolute value of any number is always non-negative. Therefore, there are no solutions for this case.

So the only solution for this equation is x = -1.

3. |-x - 1| * (|x| - 1) = 0

Similar to the previous equation, we consider both cases:

Case 1: |-x - 1| = 0

If |-x - 1| = 0, it means that -x - 1 = 0. Solving for x, we have:

-x - 1 = 0 => x = -1

Case 2: |x| - 1 = 0

If |x| - 1 = 0, it means that |x| = 1. Solving for x, we have:

x = 1 or x = -1

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

4. -|-x| * (2 - x) = 0

Again, we consider each factor separately:

Case 1: -|-x| = 0

If -|-x| = 0, it means that |-x| = 0. The absolute value of any number is non-negative, so the only solution is x = 0.

Case 2: 2 - x = 0

Solving for x, we have:

2 - x = 0 => x = 2

So the solutions for this equation are x = 0 and x = 2.

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

We set each factor equal to zero and solve for x separately:

Case 1: |x| + 1 = 0

If |x| + 1 = 0, it means that |x| = -1, which is not possible. Therefore, there are no solutions for this case.

Case 2: 2 - x = 0

Solving for x, we have:

2 - x = 0 => x = 2

So the only solution for this equation is x = 2.

To summarize the solutions for each equation:

1. x = 3, x = 0
2. x = -1
3. x = -1, x = 1
4. x = 0, x = 2
5. x = 2