Question

已知m^2+9n^2+4m-6n+5=0,求m,n的值

Answer 1

m^2+9n^2+4m-6n+5=0,

m^2+4m+4+9n^2-6n+1=0,

(m+2)²+(3n-1)²=0,

(m+2)²>=0,(3n-1)²>=0,

所以(m+2)²=0,m=-2;(3n-1)²=0,n=1/3;

（2m-3n)^2-(2m+3n)(2m-3n)+(2m+3n)^2

=[（2m-3n)-(2m+3n)]²+(2m+3n)(2m-3n)

=[2m-3n-2m-3n)]²+(2m)²-(3n)²

=[-6n)]²+(2m)²-(3n)²

=[-6/3)]²+(-4)²-(1)²

=4+16-1

=19

或

（2m-3n)^2-(2m+3n)(2m-3n)+(2m+3n)^2

=（-4-1)^2-(-4+1)(-4-1)+(-4+1)^2

=25-15+9

=19