Розділ 4. ЛІНІЙНІ РІВНЯННЯ ТА СИСТЕМИ » 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 = 13/3 або x = –3. x = 41/3. 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 = 8/12; x = 2/3.