Question

(x-5)(x-3)(x+3)(x+1)=-35
помогите с уравнением (НЕ ГРАФИК)

Answer 1

(x-5)(x-3)(x+3)(x+1)=-35

(x-5)(x+3)(x-3)(x+1)=-35

(x² - 5x + 3x - 15)(x² - 3x + x - 3) = -35
(x² - 2x - 15)(x² - 2x - 3) = -35
x² - 2x - 3 = y
(y - 12)y = -35
y² - 12y + 35 = 0
D = 12² - 4*35*1 = 144 - 140 = 4
y₁₂ = (12 +- 2)/2 = 7  5
1. y₁ = 5

x² - 2x - 3 = 5
x² - 2x - 8 = 0
D = 4 + 32 = 36
x₁₂ = (2 +- 6)/2 =  -2   4
x₁ = -2
x₂ = 4
2. y₂ = 7

x² - 2x - 3 = 7
x² - 2x - 10 = 0
D = 4 + 40 = 44
x₃₄ = (2 +- √44)/2 = (2 +- 2√11)/2 =   (1 + √11),   (1 - √11)
x₃ = 1 + √11
x₄ = 1 - √11
ответ x = {1 ± √11, -2, 4}