初一数学题两道(同底数幂)求详细步骤
问题描述:
初一数学题两道(同底数幂)求详细步骤
1m²+m-1=0,求m³+2m²+2010
2x²+x-2009=0,求x³-2010x+2010
答
1.因为m²+m-1=0,所以m²+m=0+1=1,
m³+2m²+2010
=m·m²+m²+m²+2010
=m·m²+m·m+m²+2010
=m(m+m²)+m²+2010
=1·m+m²+2010
=m²+m+2010
=1+2010
=2011
2.因为x²+x-2009=0,所以x²+x=2009
x³-2010x+2010
=x³+x²-x²-2010x+2010
=x²x+x·x-x²-2010x+2010
=x(x²+x)-x²-2010x+2010
=2009x-x²-2010x+2010
=-x²-x+2010
=-(x²+x)+2010
=-2009+2010
=1