Question

已知:x=2-根号5,则x^4-8x^3+16x^2-x+1=

Answer 1

x=2-√5,x-2=-√5.

x^4-8x^3+16x^2-x+1

=(x^4-4x^3+4x^2)-4x^3+12x^2-x+1

=x^2(x-2)^2-4x^3+12x^2-x+1

=5x^2-4x^3+12x^2-x+1

=-4x^3+17x^2-x+1

=-4x^3+16x^2-16x+x^2+15x+1

=-4x(x-2)^2+x^2+15x+1

=-20x+x^2+15x+1

=x^2-5x+1

=9-4√5-5(2-√5)+1

=√5