532. Решите уравнение: a) 3x² - 7x + 4 = 0; б) 5x² - 8x + 3 = 0; в) 3x² - 13х + 14 = 0; г) 2y² - 9у + 10 = 0; д) 5y² - 6y + 1 = 0; e) 4x² + x - 33 = 0; ж) у² - 10у - 24 = 0; з) p² + p - 90 = 0.

a) 3x² - 7x + 4 = 0

D = b² - 4ac = (-7)² - 4 * 3 * 4 = 49 - 48 = 1

x1 = (-b + √D) / 2a = (7 + 1) / (2 * 3) = 8 / 6 = 4 / 3

x2 = (-b - √D) / 2a = (7 - 1) / (2 * 3) = 6 / 6 = 1

б) 5x² - 8x + 3 = 0

D = b² - 4ac = (-8)² - 4 * 5 * 3 = 64 - 60 = 4

x1 = (-b + √D) / 2a = (8 + 2) / (2 * 5) = 10 / 10 = 1

x2 = (-b - √D) / 2a = (8 - 2) / (2 * 5) = 6 / 10 = 3 / 5

в) 3x² - 13х + 14 = 0

D = b² - 4ac = (-13)² - 4 * 3 * 14 = 169 - 168 = 1

x1 = (-b + √D) / 2a = (13 + 1) / (2 * 3) = 14 / 6 = 7 / 3

x2 = (-b - √D) / 2a = (13 - 1) / (2 * 3) = 12 / 6 = 2

г) 2y² - 9у + 10 = 0

D = b² - 4ac = (-9)² - 4 * 2 * 10 = 81 - 80 = 1

y1 = (-b + √D) / 2a = (9 + 1) / (2 * 2) = 10 / 4 = 5 / 2

y2 = (-b - √D) / 2a = (9 - 1) / (2 * 2) = 8 / 4 = 2

д) 5y² - 6y + 1 = 0

D = b² - 4ac = (-6)² - 4 * 5 * 1 = 36 - 20 = 16

y1 = (-b + √D) / 2a = (6 + 4) / (2 * 5) = 10 / 10 = 1

y2 = (-b - √D) / 2a = (6 - 4) / (2 * 5) = 2 / 10 = 1 / 5

e) 4x² + x - 33 = 0

D = b² - 4ac = 1² - 4 * 4 * (-33) = 1 + 528 = 529

x1 = (-b + √D) / 2a = (-1 + 23) / (2 * 4) = 22 / 8 = 11 / 4

x2 = (-b - √D) / 2a = (-1 - 23) / (2 * 4) = -24 / 8 = -3

ж) у² - 10у - 24 = 0

D = b² - 4ac = (-10)² - 4 * 1 * (-24) = 100 + 96 = 196

y1 = (-b + √D) / 2a = (10 + 14) / (2 * 1) = 24 / 2 = 12

y2 = (-b - √D) / 2a = (10 - 14) / (2 * 1) = -4 / 2 = -2

з) p² + p - 90 = 0.

D = b² - 4ac = 1² - 4 * 1 * (-90) = 1 + 360 = 361

p1 = (-b + √D) / 2a = (-1 + 19) / (2 * 1) = 18 / 2 = 9

p2 = (-b - √D) / 2a = (-1 - 19) / (2 * 1) = -20 / 2 = -10

Ответ: a) x1 = 4 / 3, x2 = 1; б) x1 = 1, x2 = 3 / 5; в) x1 = 7 / 3, x2 = 2; г) y1 = 5 / 2, y2 = 2; д) y1 = 1, y2 = 1 / 5; e) x1 = 11 / 4, x2 = -3; ж) y1 = 12, y2 = -2; з) p1 = 9, p2 = -10