Розділ 4. ЛІНІЙНІ РІВНЯННЯ ТА СИСТЕМИ » 841

Знайди корені рівняння. a) 4 – (x – 3)2 = 0; 22 – (x – 3)2 = 0; (2 – (x – 3))(2 + x – 3) = 0; (2 – x + 3)(x – 1) = 0; (5 – x)(x – 1) = 0; 5 – x = 0 або x – 1 = 0; x = 5 x = 1. б) (5x + 4)2 = 196; (5x + 4)2 – 196 = 0; (5x + 4)2 – 142 = 0; (5x + 4 – 14)(5x + 4 + 14) = 0; (5x – 10)(5x + 18) = 0; 5x – 10 = 0 або 5x + 18 = 0; 5x = 10 або 5x = –18; x = 2 або x = –3,6. в) (3x – 2)2 – (x + 6)2 = 0; (3x – 2 – (x + 6))(3x – 2 + x + 6) = 0; (3x – 2 – x – 6)(4x + 4) = 0; (2x – 8)(4x + 4) = 0; 2x – 8 = 0 або 4x + 4 = 0; 2x = 8 або 4x = –4; x = 4 x = –1. г) (2x – 1)2 = (4 –5x)2; (2x – 1)2 – (4 – 5x)2 = 0; (2x – 1 – (4 – 5x))(2x – 1 + 4 – 5x) = 0; (2x – 1 – 4 + 5x)(3 – 3x) = 0; (7x – 5)(3 – 3x) = 0; 7x – 5 = 0 або 3 – 3x = 0; 7x = 5 або –3x – 3|: (–3); x = 5/7 або х = 1. ґ) (2x + 1)(4x2 – 2x + 1) = 4x(2x2 – 5); 8x3 – 4x2 + 2x + 4x2 – 2x + 1 = 8x3 – 20x; 20x = –1; x = –0,05. д) x(8x2 – 5) = (4x2 – 10x + 25)(2x + 5); 8x3 – 5x = 8x3 – 20x2 + 50x + 20x2 – 50x + 125; –5x = 125|: (–5); x = –25.