由已知3x²-x=1得3x² = x +1,多次代入原式以降次得
原式=9x^4+12x³-3x²-7x+2000
=(3x²)²+ (3x²)*4x -3x²-7x+2000
=(x +1)²+ (x +1)*4x -(x +1)-7x+2000
=5x²-2x+2000
=(5/3)*3x²-2x+2000
=(5/3)* (x +1)-2x+2000
=[(5- x )/3]+2000
再由已知3x²-x=1得3x² - x -1=0,解方程得x=(1±√13)/6,代入上面化简后的结果得
原式=(1/3)*[ 5-(1±√13)/6 ]+2000=[ (29±√13)/18 ]+2000