题目

设x=√3 -2,则x^6+3x^5+11x^3+2x+1=_____

提问时间：2020-12-10

答案

x^6+3x^5+11x^3+2x+1
=x^3*(x^3+3x^2+11)+2x+1
=x^3*[(x^2*(x+3)+11]+2x+1
=x^3*[(x^2*(√3 -2+3)+11]+2x+1
=x^3*[(x^2*(√3 +1)+11]+2x+1
=x^3*[(√3 -2)*(√3 -2)*(√3 +1)+11]+2x+1
=x^3*[(√3 -2)*(1-√3)+11]+2x+1
=x^3*[(√3 -2)*(1-√3)+11]+2x+1
=x^3*[-5+3√3+11]+2x+1
=x^3*(6+3√3)+2x+1
=3x^3*(2+√3)+2x+1
=3*(√3 -2)*(√3 -2)*(√3 -2)*(√3+2)+2x+1
=-3*(√3 -2)*(√3 -2)+2*(√3 -2)+1
=-3*(7-4√3)+2√3 -3
=-24+14√3