Question

若x^2-2x+y^2-4y+5=0,求9x^2y^2-12x^3y^2+4x^4y^2的值

Answer 1

x^2-2x+y^2-4y+5=0

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

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

所以x-1=0,y-2=0

x=1,y=2

9x^2y^2-12x^3y^2+4x^4y^2

=x^2y^2(9-12x+4x^2)

=x^2y^2(2x-3)^2

=1*4*(2-3)^2

=4