已知x=16/(根号17+1),求x^3+2x^2-17x-3+16/x的值

问题描述:

已知x=16/(根号17+1),求x^3+2x^2-17x-3+16/x的值

x=16/(根号17+1)=√17-1
所以
x+1=√17
x²+2x+1=17
x²+2x=16
x+2=16/x
x^3+2x^2-17x-3+16/x
=x^3+2x^2+x-18x-3+16/x
=x(x²+2x+1)-18x-3+16/x
=17x-18x-3+16/x
=-x-3+16/x
=-x-3+x+2
=-1