Question

急！！已知3x的平方-x=1, 求代数式6x的三次方+7x的平方-5x+2006的值

RT。。。
谢了。请给出解题过程和简单的分析过程。。。
好的加20分。谢谢- -

Answer 1

因3X2-X=1，故6X3+7X2-5X+2006
=6X3-2X2+9X2-5X+2006
=2X(3X2-X)+9X2-3X-2X+2006
=2X×1+3(3X2-X)-2X+2006
=2X+3-2X+2006
=2009

Answer 2

6x^3+7x^2-5x+2006
=x[6x^2+7x-5]+2006
=x[2x-1][3x+5]+2006
=[2x-1][3x^2+5x]+2006
=[2x-1][1+x+5x]+2006
=[2x-1][6x+1]+2006
=12x^2-4x-1+2006
=4[3x^2-x]+2005
=4*1+2005
=2009

Answer 3

3x^2-x=1
3x^3-x^2=x
3x^3=x^2+x
6x^3+7x^2-5x+2006
=2(x^2+x)+7x^2-5x+2006
=9x^2-3x+2006
=3(3x^2-x)+2006
=3*1+2006
=2009