![1)|x^{2}-x|=0\\x^{2}-x=0\\x(x-1)=0\\x_{1} =0\\x-1=0\\x_{2}=1 1)|x^{2}-x|=0\\x^{2}-x=0\\x(x-1)=0\\x_{1} =0\\x-1=0\\x_{2}=1](https://tex.z-dn.net/?f=1%29%7Cx%5E%7B2%7D-x%7C%3D0%5C%5Cx%5E%7B2%7D-x%3D0%5C%5Cx%28x-1%29%3D0%5C%5Cx_%7B1%7D%20%3D0%5C%5Cx-1%3D0%5C%5Cx_%7B2%7D%3D1)
2) ||x - 1| - 4| = 3
Раскроем первый модуль:
|x - 1| - 4 = 3 или |x - 1| - 4 = - 3
|x - 1| = 7 |x - 1| = 1
Раскроем модули :
x - 1 = 7 или x - 1 = - 1 x - 1 = 1 или x - 1 = - 1
x₁ = 8 x₂ = 0 x₃ = 2 x₄ = 0
Ответ : 0 ; 2 ; 8
3) |||x - 3| - 3| - 3| = 3
||x - 3| - 3| - 3 = 3 или ||x - 3| - 3| - 3 = - 3
||x - 3| - 3| = 6 ||x - 3| - 3| = 0
|x - 3| - 3 = 6 или |x - 3| - 3 = - 6 |x - 3| - 3 = 0
|x - 3| = 9 |x - 3| = - 3 - решений нет |x - 3| = 3
x - 3 = 9 или x - 3 = - 9 x - 3 = 3 или x - 3 = - 3
x₁ = 12 x₂ = - 6 x₃ = 6 x₄ = 0
Ответ : - 6 ; 0 ; 6 ; 12