若实数x,y满足x^2+y^2+8x-6y+16=0求x+y的最小值

x^2+y^2+8x-6y+16=0
(x²+8x+16)+(y²-6y+9)=9
(x+4)²+(y-3)²=3²
令x=-4+3cosa,y=3+3sina
x+y
=-4+3cosa+3+3sina
=3(sina+cosa)-1
=3(根号2)sin(a+45)-1

因为-1=<sin(a+45)<=1
所以-3根号2-1=<3(根号2)sin(a+45)<=3根号2-1
即x+y的最小值是：-3根号2-1

x^2+y^2+8x-6y+16=0
(x+4)^2+(y-3)^2=0
则
x=-4
y=3
x+y=-1