4x^2+4x+y^2-2y+2=0,则x^3y-y^3x得值是?

题目

4x^2+4x+y^2-2y+2=0,则x^3y-y^3x得值是?
若x^2(x-3)+3x-9能被x-a整除,则a的值是多少?

答案

4x^2+4x+y^2-2y+2= (4x^2+4x+1)+(y^2-2y+1)=(2x+1)^2+(y-1)^2=0
2x+1=0,y-1=0,x=-1/2,y=1
x^3y-y^3x=xy(x+y)(x-y)=-1/2*1/2(-3/2)=3/8
x^2(x-3)+3x-9=x^2(x-3)+3(x-3)=(x-3)(x^2+3) a=3