7年级数学题目各位帮忙解答些数学题目(要求写出过程1.已知10^m=5,10^n=4,求10^(2m-3n)的值2.已知3^x=a,3^y=b,求27^(2x-3y)3.已知x=2a-b-c,y=2b-c-a,z=2c-a-b,求x(b-c)+y(c-a)+z(a-b)的值4.已知m^2+m-1=0,求代数试m^3+2(m^2)+

Question

7年级数学题目
各位帮忙解答些数学题目(要求写出过程
1.已知10^m=5,10^n=4,求10^(2m-3n)的值
2.已知3^x=a,3^y=b,求27^(2x-3y)
3.已知x=2a-b-c,y=2b-c-a,z=2c-a-b,求x(b-c)+y(c-a)+z(a-b)的值
4.已知m^2+m-1=0,求代数试m^3+2(m^2)+2006的值

Answer 1

1 10^(2m-3n)
=10^2m/10^3n
因为10^m=5,10^n=4
10^2m=(10^m)^2=25
10^3n=(10^n)^3=4^3=64
所以10^(2m-3n)=25/64
2 27^(2x-3y)
=27^2x/27^3y
=3^6x/3^9y
3^6x=(3^x)^6=a^6
3^9y=(3^y)^9=b^9
所以27^(2x-3y)=a^6/b^9
3 因为x=2a-b-c,y=2b-c-a,z=2c-a-b,
x(b-c)+y(c-a)+z(a-b)
=(2a-b-c)(b-c)+(2b-c-a)(c-a)+(2c-a-b)(a-b)
=2a(b-c)-(b^2-c^2)+2b(c-a)-(c^2-a^2)+2c(a-b)-(a^2-b^2)
=2ab-2ac-b^2+c^2+2bc-2ab-c^2+a^2+2ac-2bc-a^2+b^2
=0
4 因为m^2+m-1=0
所以m^2+m=1
m^3+2(m^2)+2006
=m^3+2(m^2)+1+2005
=m^3+2(m^2)+m^2+m+2005
=m^3+3(m^3)+m+2005
=m(m^2+3m+1)+2005
=m(m^2+m+2m+1)+2005
=m(1+2m+1)+2005
=m(2+2m)+2005
=2m+2m^2+2005
=2(m^2+m)+2005
=2+2005
=2007