已知x^2+y^2-4x+6y+13=0,求x^2-6xy+9y^2的值

已知x^2+y^2-4x+6y+13=0,求x^2-6xy+9y^2的值
已知x^2+y^2-4x+6y+13=0,求x^2-6xy+9y^2的值

已知x^2+y^2-4x+6y+13=0,求x^2-6xy+9y^2的值
x^2+y^2-4x+6y+13=0
(x-2)^2+(y+3)^2=0
由非负性
x-2=0
y+3=0
解得
x=2
y=-3
则
x^2-6xy+9y^2
=(x-3y)^2
=(2+9)^2
=11^2
=121

121