Question

解方程x^4 +3x^3-5x-3=0

Answer 1

x^4+3x^3-5x-3 = 0 ,

(x^4+2x^3+x^2)+(x^3+2x^2+x)-3(x^2+2x+1) = 0 ,

x^2*(x^2+2x+1)+x(x^2+2x+1)-3(x^2+2x+1) = 0 ,

(x^2+2x+1)(x^2+x-3) = 0 ,

(x+1)^2*(x^2+x-3) = 0 ,

所以 x1 = x2 = -1 ,x3 = (-1-√13)/2,x4 = (-1+√13)/2 .