Question

已知a,b满足a^2+b^2+4a-8b+20=0,试分解(x^2+y^2)-(b+axy).

Answer 1

a^2+b^2+4a-8b+20=0

(a^2+4a+4)+(b^2-8b+16)=0

即(a+2)^2+(b-4)^2=0

可得a=-2,b=4

代回为x^2+y^2-4-2axy=(x-y)^2-4=(x-y-2)(x-y+2)