Question

解方程x的四次方+2x的立方-6x的平方+2x+1=0

Answer 1

原式可化为：x^4+2x^3-6x^2+2x-1=0

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

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

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

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

(x-1)[x(x+4)(x-1)+(x--1)]=0

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

(x-1)^2[x-(-2+√3)][x-(-2-√3)]=0

所以：x=1 x=-2+√3 x=-2-√3