Question

Х(х+1)(х+3)(х+4)=40. Помогите решить

Answer 1

X*(x+1)*(x+3)*(x+4)=40
(x^2+x)*(x+3)*(x+4)=40
(x^3+3x^2+x^2+3x)*(x+4)=40
(x^3+4x^2+3x)*(x+4)=40
x^4+4x^3+4x^3+16x^2+3x^2+12x=40
x^4+8x^3×19^2+12x=40
x^4+8x^3+19x^2+12x-40=0
x^4-x^3+9x^3-9x^2+28x^2-28x+40x-40=0
x^3*(x-1)+9x^2*(x-1)+40(x-1)=0
(x-1)*(x^3+9x^2+28x+40)=0
(x-1)*(x^3+5x^2+4x^2+20x+8x+40)=0
(x-1)*(x^2*(x+5)×4x*(x+5)+8(x+5))=0
(x-1)*(x+5)*(x^2+4x+8)=0
x-1=0
x+5=0
x^2+4x+8=0
x=1
x=-5

x1=-5
x2=1