Question

若x²+y²-2x+6y+10=0,则x+y=( );xy=( )?

若x²+y²-2x+6y+10=0,则x+y=( );xy=( )?
亲们详细讲解，谢谢了

Answer 1

x²+y²-2x+6y+10=0
(x²-2x+1)+(y²+6y+9)=0
(x-1)²+(y+3)²=0
∵(x-1)²≥0.(y-3)²≥0
∴(x-1)²=0.(y-3)²=0
∴x-1=0.y-3=0
∴x=1.y=-3
∴x+y=1-3=-2
xy=-3

Answer 2

化简
x²+y²-2x+6y+10=0
x²-2x+y²+6y+1+9=0
x²-2x+1+y²+6y+9=0
(x-1)²+(y+3)²=0

因为(x-1)²≧0
(y+3)²≧0
所以(x-1)²=0 x=1
(y+3)²=0 y=-3

所以x+y=1-3=-2
xy=1×(-3)=-3

Answer 3

Answer 4