Помогите

[петровна]

а) х|х|+х-2=2|х|

|х-3|+|х-4|=2х+1

|4х-1|-|2х-3|+|х-2|=0

|2-|1-|х|||=1

[fortpost]

а) х|х|+х-2=2|х|

1. x ≥ 0; x² + x - 2 = 2x; x² - x - 2 = 0; x_1,2 = 1/2 ± √(1/4+2) = 1/2 ± √9/4 = 1/2 ± 3/2
x₁ = 2, x₂ = -1 - не подходит.

2. x < 0; -x² + x - 2 = -2x; x² - 3x + 2 = 0; x_1,2 = 3/2 ± √(9/4-2) = 3/2 ± √1/4 = 3/2 ± 1/2
x₁ = 2, x₂ = 1 - не подходят оба.

[fortpost]

б) |х-3|+|х-4|=2х+1

1. x < 3; 3 - x + 4 - x = 2x + 1; 7 - 2x = 2x + 1; 6 = 4x; x = 6/4 = 1,5

2. 3 ≤ x ≤ 4; x - 3 + 4 - x = 2x + 1; 1 = 2x + 1; 0 = 2x; x = 0 - не подходит

3. x > 4; x - 3 + x - 4 = 2x + 1; 2x -7 = 2x + 1; -7 = 1 - нет решений

[fortpost]

в) |4х-1|-|2х-3|+|х-2|=0

1. x < 1/4; 1 - 4x + 2x - 3 + 2 - x = 0; -3x = 0; x = 0

2. 1/4 ≤ x ≤ 3/2; 4x - 1 + 2x - 3 + 2 - x = 0; 5x - 2 = 0; x = 2/5

3. 3/2 ≤ x ≤ 2; 4x - 1 - 2x + 3 + 2 - x = 0; x + 4 = 0; x = -4 - не подходит

4. x > 2; 4x - 1 - 2x + 3 + x - 2 = 0; 3x = 0; x = 0 - не подходит

[fortpost]

г) |2-|1-|х|||=1

1. |1 - |х|| < 2; 2 - |1 - |х|| = 1; |1-|х|||=1

1.1. |х| < 1; 1 - |х| = 1; x = 0

1.2. |х| ≥ 1; |х| - 1 = 1; |х| = 2; x = ±2


2. |1 - |х|| ≥ 2; |1 - |х|| - 2 = 1; |1 - |х|| = 3;

2.1. |х| < 1; 1 - |х| = 3; |х| = -2 - решений нет

2.2. |х| ≥ 1; |х| - 1 = 3; |х| = 4; x = ±4