Question

设实数x,y满足x^2+y^2+8x+6y+25=0,求(x^2-4y^2)/(x^2+4xy+4y^2)-x/x+2y

Answer 1

x^2+y^2+8x+6y+25

=(x+4)^2+(y+3)^2=0

则x+4=0

y+3=0

(x^2-4y^2)/(x^2+4xy+4y^2)-x/(x+2y)

=[（x+2y）（x-2y）]/(x+2y)^2-x/(x+2y)

=（x-2y）/(x+2y)-x/(x+2y)

=-2y/(x+2y)

=6/-10

=-3/5