Question

已知：X的平方减去X减去1等于0,求代数式负X的三次方加2X的二次方加2009的值

Answer 1

x^2-x-1=0,

x^2-x=1.(1)

又有x^2=x+1,

x^3=x^2+x.(2).

-x^3+2x^2+2009

=-x^2-x+2x^2+2009[(2)代入]

=x^2-x+2009

=1+2009[(1)代入]

=2010.