若x=根号5+2,求x³-3x²-5x+2007的值.
问题描述：
若x=根号5+2,求x³-3x²-5x+2007的值.
答
9倍根号5＋2026
答
x=√5+2
x-2=√5
x³-3x²-5x+2007
=x³-2x²-x²+2x-7x+14+1993
=x²(x-2)-x(x-2)-7(x-2)+1993
=√5x²-√5x-7√5+1993
=√5x²-2√5x+√5x-2√5-5√5+1993
=√5x(x-2)+√5(x-2)-5√5+1993
=5x+5-5√5+1993
=5√5+10+5-5√5+1993
=2008
答
x³-3x²-5x+2007
=(x³-3x²-4x)-x+2007
=x(x²-3x-4)-x+2007
=x(x-4)(x+1)-x+2007
=(√5+2)(√5+2-4)(√5+2+1)-(√5+2)+2007
=(√5+2)(√5-2)(√5+3)-√5-2+2007
=(5-4)(√5+3)-√5+2005
=√5+3-√5+2005
=2008