Question

已知4x^2+y^2-4x+6y+10=0,求4x^2-12xy+9y^2的值

Answer 1

4x^2+y^2-4x+6y+10=0

(4x^2-4x+1)+(y^2+6y+9)=0

(2x-1)^2+(y+3)^2=0

x=1/2,y=-3

4x^2-12xy+9y^2

=(2x-3y)^2

=[2*1/2-3*(-3)]^2

=(1+9)^2

=100