已知x=13/(4+根号3),求(x^4-6x^3-2x^2+18x+23)/(x^2-8x+15) 的值
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
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
赞 miyuhao 幼苗
共回答了13个问题采纳率：92.3% 举报
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
=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
1年前
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