Вправи: 840

840. Знайди корені рівняння.

a) (x + 1)² – 9 = 0;

(x + 1 – 3)(x + 1 + 3) = 0;

(x – 2)(x + 4) = 0;

x – 2 = 0 або x + 4 = 0;

x = 2 або х = –4.

б) (3x – 2)² = 121;

(3x – 2)² – 121 = 0;

(3x – 2 – 11)(3x – 2 + 11) = 0;

(3x – 13)(3x + 9) = 0;

3x – 13 = 0 або 3x + 9 = 0;

3x = 13 або 3x = –9;

x = 133 або x = –3.

x = 413.

в) (x – 1)2 – (3 – x)2 = 0;

(x – 1 – (3 – x)2 = 0;

(x – 1 – 3 + x) • 2 = 0;

(2x – 4) • 2 = 0;

4x = 8|: 4;

x = 2.

г) (4x – 10)² = (3x – 4)²;

(4x – 10)² – (3x – 4)² = 0;

(4x – 10 – (3x – 4))(4x – 10 + 3x – 4) = 0;

(4x – 10 – 3x + 4)(7x – 14) = 0;

(x – 6)(7x – 14) = 0;

x – 6 = 0 або 7x – 14 = 0;

x = 6 або 7х = 14;

х = 2.

ґ) (x² + x + 1)(x – 1) = x(x² + 1);

x³ + x² + x – x² – x – 1 = x³ + x;

–x = 1;

x = –1.

д) (9x² + 4) • 3x = (3x + 2)(9x² – 6x + 4);

27x³ + 12x = 27x³ – 18x² + 12x + 18x² – 12x + 8;

12x = 8|: 12;

x = 812;

x = 23.