若x^2+2x+y^2-6y+10=0,求x^3y的值

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若x^2+2x+y^2-6y+10=0,求x^3y的值

若x^2+2x+y^2-6y+10=0,求x^3y的值
若x^2+2x+y^2-6y+10=0,求x^3y的值

若x^2+2x+y^2-6y+10=0,求x^3y的值
x^2+2x+y^2-6y+10
=x^2+2x+1+y^2-6y+9
=(x+1)^2+(y-3)^2
=0
得出x=-1 y=3
所以x^3y=-3

x^2+2x+y^2-6y+10=0配方得,(X+1)^2+(y-3)^2=0
x=-1.y=3 x^3y=-1

x^2+2x+y^2-6y+10=0,
=>(x^2+2x+1)+(y^2-6y+9)=0
=> (x+1)^2+(y-3)^2=0
都是平方,所以最小值为0
x+1=0, y-3=0
x=-1, y=3
x^3y=(-1)^9=-1

(x^2+2x+1)+(y^2-6y+9)=0
(x+1)^2+(y-3)^2=0
x+1=0,y-3=0
x=-1,y=3
x^(3y)=(-1)^9=-1