已知x=根号5-根号2 分之2根号2+根号5,求x五次方-7x四次方+6x三次方-7x²+11x+13

x=根号5-根号2 分之2根号2+根号5=[(2√ 2+√ 5)(√ 5+√ 2)]/[(√ 5-√ 2)(√5+√2)]=3+√ 10,
x五次方-7x四次方+6x三次方-7x²+11x+13
=x^5+x^3-(7x^4+7x^2)+(5x^3+5x)+6x+13
=x^3(x^2+1)-7x^2(x^2+1)+5x(x^2+1)+6x+13
=(x^2+1)(x^3-7x^2+5x)+6x+13
=(x^2+1)*x*(x^2-7x+5)+6x+13
=(20+6√ 10)(3+√ 10)(3-√ 10)+6(3+√10)+13
=(20+6√ 10)(-1)+18+6√ 10+13
=11