x=1/(2-√5)
x=(2+√5)/(2-√5)(2+√5)
x=-2-√5
x^3+3x^2-5x+1
=x^3+3x^2-4x-x+1
=x(x^2+3x-4)-(x-1)
=x(x-1)(x+4)-(x-1)
=(x-1)(x^2+4x-1)
=(x-1)(x^2+4x+4-5)
=(x-1)[(x+2)^2-5]
=(x-1)[(-2-√5+2)^2-5]
=(x-1)[(-√5)^2-5]
=(x-1)(5-5)
=0