Question

СРОЧНО!!!! помогите (x+3)(x-1)(x+2)(x+6)=-20

Answer 1

Объяснение:

$(x+3)(x-1)(x+2)(x+6)=-20\\\\((x+3)(x+2))*(x-1)(x+6)=-20\\\\(x^2+3x+2x+6)*(x^2-x+6x-6)=-20\\\\(x^2+5x+6)*(x^2+5x-6)=-20.$

Пусть х²+5х=t       ⇒

(t+6)*(t-6)=-20

t²-6²=-20

t²-36=-20

t²=16

t₁=-4    t₂=4

$1)\ t_1=-4\\\\x^2+5x=-4\\\\x^2+5x+4=0\\\\x^2+4x+x+4=0\\\\x*(x+4)+(x+4)=0\\\\(x+4)*(x+1)=0\\\\x+4=0\\\\x_1=-4.\\\\x+1=0\\\\x_2=-1$

$\displaystyle\\2)\ t_2=4\\\\x^2+5x=4\\\\x^2+5x-4=0\\\\D=(-5)^2-4*1*(-4)=25+16=41\\\\\sqrt{D} =\sqrt{41} \\\\x_{3,4}=\frac{-5б\sqrt{41} }{2} \\\\x_3=\frac{-5-\sqrt{41} }{2} \approx-5,7\\\\x_4=\frac{-5+\sqrt{41} }{2}\approx0,7.$

Ответ: x₁=-4,    x₂=-1,     x₃=(-5-√41)/2,     x₄=(-5+√41)/2.