x²+y²+2x-8y+17=0,求x的2009次方+xy

x²+y²+2x-8y+17=0,求x的2009次方+xy
x²+y²+2x-8y+17=0,求x的2009次方+xy

x²+y²+2x-8y+17=0,求x的2009次方+xy
x²+y²+2x-8y+17=0
(x+1)²+(y-4)²=0
∴x=-1 y=4
x的2009次方+xy=（-1）的2009次方+（-1）×4=-1-4=-5

x²+2x+1+y²-8y+16=0
(x+1)²+(y-4)²=0
x=-1 y=4
x的2009次方+xy=-1+-4=-5

即(x²+2x+1)+(y²-8y+16)=0
(x+1)²+(y-4)²=0
所以x+1=0,y-4=0
x=-1,y=4
所以原式=-1-4=-5