Question

已知x=13/(4+根号3),求(x^4-6x^3-2x^2+18x+23)/(x^2-8x+15) 的值

Answer 1

x^4-6x^3-2x^2+18x+23

=x^2(x^2-8x+13)+2x^3-15x^2+18x+23

=2x(x^2-8x+13)+x^2-8x+23

=x^2-8x+23

x^4-6x^3-2x^2+18x+23

=x^4-8x^3+2x^3+13x^2-15x^2+18x+23

=x^4-8x^3+13x^2+2x^3-15x^2+18x+23

=x^2(x^2-8x+13)+2x^3-15x^2+18x+23

=x^2*(0)+2x^3-15x^2+18x+23

=2x^3-15x^2+18x+23

=2x^3-16x^2+x^2+26x-8x+23

=2x^3-16x^2+26x+x^2-8x+23

=2x(x^2-8x+13)+x^2-8x+23

=2x*(0)+x^2-8x+23

=x^2-8x+23