4 (x+1) * (x+2) * (x+3) * (x+6) = - 3x^2

Question

Математика

Светланыч

21 июля, 17:57

4 (x+1) * (x+2) * (x+3) * (x+6) = - 3x^2

+5

Ответы (1)

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Созонт · Answer 1

4 (x+1) (x+6) * (x+2) (x+3) = - 3x^2

4 (x^2 + 7x + 6) * (x^2 + 5x + 6) = - 3x^2

Замена x^2 + 6x + 6 = t

4 (t + x) (t - x) = - 3x^2

4 (t^2 - x^2) = - 3x^2

4t^2 - 4x^2 + 3x^2 = 0

4t^2 - x^2 = 0

(2t - x) (2t + x) = 0

Обратная замена

(2x^2 + 12x + 12 - x) (2x^2 + 12x + 12 + x) = 0

(2x^2 + 11x + 12) (2x^2 + 13x + 12) = 0

1) 2x^2 + 11x + 12 = 0

D = 11^2 - 4*2*12 = 121 - 96 = 25 = 5^2

x1 = (-11 - 5) / 4 = - 16/4 = - 4

x2 = (-11 + 5) / 4 = - 6/4 = - 1,5

2) 2x^2 + 13x + 12 = 0

D = 13^2 - 4*2*12 = 169 - 96 = 73

x3 = (-13 - √73) / 4

x4 = (-13 + √73) / 4