已知3x^2-x=1,求6x^3+7x^2-5x+2001的值

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已知3x^2-x=1,求6x^3+7x^2-5x+2001的值
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已知3x^2-x=1,求6x^3+7x^2-5x+2001的值
已知3x^2-x=1,求6x^3+7x^2-5x+2001的值

已知3x^2-x=1,求6x^3+7x^2-5x+2001的值
3x^2-x=1
6x^3+7x^2-5x+2001
=6x^3-2x^2+9x^2-5x+2001
=2x(3x^2-x)+9x^2-5x+2001
=2x+9x^2-5x+2001
=9x^2-3x+2001
=3(3x^2-1)+2001
=3*1+2001
=2004

因为3x^2-x=1,
所以3x^2-x-1=0,
所以6x^3+7x^2-5x+2001
=2x(3x^2-x-1)+9x^2-3x+2001
=2x*0+3(3x^2-x-1)+2004
=3*0+2004
=2004.

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