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

题目

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

答案

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