X(x+2)(x+3)(x+5)=72 помогите пож

Question

X(x+2)(x+3)(x+5)=72 помогите пож

Answer 1

X(x+5)(x+2)(x+3) = 72
(x² + 5x)(x² + 5x + 6) = 72

x² + 5x = t

t(t+6) = 72
t²+ 6t - 72 = 0
D = 36 + 288 = 324 = 18²
t1 = (-6-18)/2 = -12
t2 = (-6+18)/2 = 6

x² + 5x = -12
x² + 5x + 12 = 0
D = 25 - 48 < 0

x² + 5x = 6
x² + 5x - 6 = 0
D = 25 + 24 = 49 = 7²

x1 = (-5-7)/2 = -6
x2 = (-5+7)/2 = 1

Ответ: -6 и 1