x²-2x+y²+8y+17=x²-2x+y²+8y+1+16=x²-2x+1+y²+8y+16=（x-1）²+（y+4）²=0
∵（x-1）²≥0,（y+4）²≥0
∴（x-1）²=0,（y+4）²=0
∴x=1 y=-4