Question

已知m^2+9n^2+6m+6n+10=0，求(m^2-6mn+9n^2)/(m-3n)-(4m^2-9n^2)/(2m-3n)

Answer 1

m^2+9n^2+6m+6n+10=0
m^2+6m+9+9n^2+6n+1=0
(m+3)^2+(3n+1)^2=0
(m+3)^2=0,(3n+1)^2=0
m=-3
n=-1/3

(m^2-6mn+9n^2)/(m-3n)-(4m^2-9n^2)/(2m-3n)
=(m-3n)^2/(m-3n)-(2m-3n)(2m+3n)/(2m-3n)
=m-3n-(2m+3n)
=m-3n-2m-3n
=-m-6n
=-(-3)-6*(-1/3)
=3+2
=5

Answer 2

m^2+9n^2+6m+6n+10=0
(m+3)²+(3n+1)²=0
所以：m+3=0；3n+1=0
解得：m=-3；n=-1/3

(m^2-6mn+9n^2)/(m-3n)-(4m^2-9n^2)/(2m-3n)
=(m-3n)²/(m-3n)-(2m+3n)(2m-3n)/(2m-3n)
=m-3n-3m-3n
=-2m-6n
=6+2
=8

Answer 3

m^2+9n^2+6m+6n+10=(m+3)^2+(3n+1)^1=0
得　m=-3, n=-1/3
(m^2-6mn+9n^2)/(m-3n)-(4m^2-9n^2)/(2m-3n)
=(m-3n)^2/(m-3n)-(2m-3n)(2m+3n)/(2m-3n)
=(m-3n)-(2m+3n)=-m-6n=3+2=5

Answer 4

已知可化为：(m+3)²+(3n+1)²=0
即有：m=-3,n=-1/3
原式=[（m-3n）²/(m-3n)]-[(2m-3n)(2m+3m)/(2m-3n)]
=(m-3n)-(2m+3n)
=-m-6n=3+2=5

Answer 5

m^2+9n^2+6m+6n+10=0
m^2+6m+9+9n^2+6n+1=0
（m+3）^2+（3n+1）^2=0
m=-3 n=-1/3
后边自己求