Сократите дробь d^1: 2 -с^1: 2 /cd^1: 2 - dc^1: 2

ответ:

объяснение:

1. x^2 - 4x - 32 = 0

d = (-4)^2 - 4 * 1 * (-32) = 16 + 128 = 144

x₁ = (4 - √144) / 2 = (4 - 12) / 2 = -4

x₂ = (4 + √144) / 2 = (4 + 12) / 2 = 8

x^2 - 4x - 32 = (x + 4) * (x - 8)

4x^2 - 15x + 9 = 0

d = (-15)^2 - 4 *4 * 9 = 225 - 144 = 81

x₁ = (15 - √81) / (2 * 4) = (15 - 9) / 8 = 0,75

x₂ = (15 + √81) / (2 * 4) = (15 + 9) / 8 = 3

4x^2 - 15x + 9 = 4 * (x - 0,75) * (x - 3) = (4x - 3) * (x - 3)

2. x^4 - 35x^2 - 36 = 0

пусть t = x^2

t^2 - 35t - 36 = 0

d = (-35)^2 - 4 * 1 * (-36) = 1225 + 144 = 1369

t₁ = (35 - √1369) / 2 = (35 - 37) / 2 = -1

t₂ = (35 + √1369) / 2 = (35 + 37) / 2 = 36

вернёмся к замене

x^2 = -1

x = ±√-1

x = ± i

x^2 = 36

x = ±6

x + 2 ≠ 0 ⇒ x ≠ -2

умножим обе части дроби на x+2

x^2 - 7x -18 = 0

x₁ = -2 - не имеет смысла

ответ : 9

3. 4a^2 + a - 3 = 0

d = 1^2 - 4 * 4 * (-3) = 1 + 48 = 49

a₁ = (-1 - √49) / (2 * 4) = (-1 - 7) / 8 = -1

a₂ = (-1 + √49) / (2 * 4) = (-1 + 7) / 8 = 0,75

4a^2 + a - 3 = 4 * (a + 1) * (a - 0,75) = (a + 1) (4a - 3)