Вправи: 788

788. Розв’яжіть рівняння:

x - 1 = 0, x = 1,

a) (x - 1)(2x - 1)(3x - 1) = 0; 2x - 1 = 0, ⟺ x = 0,5,

3x - 1 = 0; x = 13;

x² = 0, x = 0,

x - 1 = 0, x = 1,

б) x2(x - 1)(x - 2)(x - 3)(x - 4) = 0; x - 2 = 0, ⟺ x = 2,

x - 3 = 0, x = 3,

x - 4 = 0; x = 4;

в) (х + 1)(х + 2)(х + 3)(х + 4) = (х + 1)(х + 2)(х + 3)(х + 5);

(х + 1)(х + 2)(х + 3)[(х + 4) - (х + 5)] = 0;

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

(х + 1)(х + 2)(х + 3) • (-1) = 0; (х + 1)(х + 2)(х + 1) = 0;

x + 1 = 0, x = -1,

x + 2 = 0, ⇔ x = -2,

x + 3 = 0; x = -3;

г) xx-1x-2(x-3)3 = xx-1x-2x-3(x-4)4;

4x(x - 1)(x - 2)(x - 3) - 3x(x - 1)(x - 2)(x - 3)(x - 4) = 0;

x(x - 1)(x - 2)(x - 3)[4 - 3(x - 4)] = 0;

x = 0, x - 1 = 0, x - 2 = 0, x - 3 = 0, 4 - 3x + 12 = 0;

⇔

x = 0,x = 1,x = 2,x = 3,-3x = -16;

⇔

x = 0,x = 1,x = 2,x = 3,x = 163; x = 513.