已知x=13/(4+根号3),求(x^4-6x^3-2x^2+18x+23)/(x^2-8x+15) 的值禁止复制粘贴：x=13_数学解答

已知x=13/(4+根号3),求(x^4-6x^3-2x^2+18x+23)/(x^2-8x+15) 的值
禁止复制粘贴：
x=13/(4+√3)=4-√3
√3=4-x
3=x²-8x+16
x^2-8x+13=0,
所以x^2-8x+15=2；
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^2-8x+13+10=10
所以：(x^4-6x^3-2x^2+18x+23)/(x^2-8x+15)=10/2=5

人气：320 ℃　时间：2019-12-18 22:43:14

解答

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