Question

已知x的平方-x-1=0,则-x的三次方+2x的平方+2009的值为多少

Answer 1

x²-x-1=0,则x²=x+1，所以-x³+2x²+2009=-x(x²)+2x²+2009=-x(x+1)+2x²+2009=-x²-x+2x²+2009
=(x²-x-1)+2010=2010

Answer 2

x(x-1)=1 =>x=1/(x-1)
-x^3+2x^2+2009
=-x^2(x-1)+x^2+2009
=-x^2(1/x)+x^2+2009
=x^2-x+2009
=x(x-1)+2009
=1+2009
=2010