计算题设x²+x-3=0求x³+4x²+2008的值

计算题设x²+x-3=0求x³+4x²+2008的值
计算题设x²+x-3=0求x³+4x²+2008的值

计算题设x²+x-3=0求x³+4x²+2008的值
由x²+x-3=0得x²+x=3
x³+4x²+2008
=x（x²+4x）+2008
=x（x²+x+3x）+2008
=x（3+3x）+2008
=3x+3x²+2008
=3（x²+x）+2008
=3x3+2008
=9+2008
=2017

x³+4x²+2008 = x(x²+x-3) +3x² + 3x + 2008
= 3(x²+x -3) +9 + 2008
= 2017

∴x²+x-3=0,即x²+x=3
∴x³+4x²+2008=x³+x²+3x²+2008
=3x+3x²+2008
=3×3+2008
=2017