若3x^2-x-1=0,求9x^4+12x^3-3x^2-7x+1999的值

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若3x^2-x-1=0,求9x^4+12x^3-3x^2-7x+1999的值
若3x^2-x-1=0,求9x^4+12x^3-3x^2-7x+1999的值

若3x^2-x-1=0,求9x^4+12x^3-3x^2-7x+1999的值
3x^2-x-1=0
(3x^2-x-1)²=0
(3x^2-x-1)²=9x^4-6x³-5x²+2x+1=0
9x^4+12x^3-3x^2-7x+1999
=(9x^4-6x³-5x²+2x+1)+18x³+2x²-9x+1998
=18x³+2x²-9x+1998
=2001-x²