Question

2的15次方x5的11次方是几位整数?要讲解， 设m的二次方+m-1等于0，求m的三次方+2m的平方+2004=？

Answer 1

2^15*5^11
=2^11*2^4*5^11
=(2*5)^11*2^4
=10^11*16
=1.6*10^12 所以是13位整数

m^2+m-1=0
m^2+m=1
m^3+2m^2+2004
=m^3+m^2+m^2+2004
=m(m^2+m)+m^2+2004
=m+m^2+2004
=1+2004=2005

Answer 2

∵m²+m-1=0
∴m²+m=1

m³+2m²+2010
=m(m²+2m)+2010
=m(m²+m+m)+2010
=m(1+m)+2010
=m+m²+2010
=1+2010
=2011

Answer 3

首先回答第二个问题，m=(-1±√5）/2，∴m³+2m²=m²(m+2)=[(-1±√5)/2]²[(-1±√5)/2+2]=(1/4)(3±√5)²=(1/8)(3±√5). ∴m³+2m²-2004=-2003.