已知X2+Y2+8X+6Y+25=0 求代数式X2++XY+4Y2分之X2-4Y2 减X+2Y分之X的值_其他解答

已知X2+Y2+8X+6Y+25=0 求代数式X2++XY+4Y2分之X2-4Y2 减X+2Y分之X的值

人气：459 ℃　时间：2020-05-21 02:33:18

解答

X2+Y2+8X+6Y+25=0
x²+8x+16+y²+6y+9=0
(x+4)²+(y+3)²=0
∴x+4=0 y+3=0
x=-4 y=-3
X2+4XY+4Y2分之X2-4Y2 减X+2Y分之X
=(x²-4y²)/(x²+4xy+4y²)-x/(x+2y)
=(x-2y)(x+2y)/(x+2y)²-x/(x+2y)
=(x-2y)/(x+2y)-x/(x+2y)
=(x-2y-x)/(x+2y)
=-2y/(x+2y)
=-2*(-3)/(-4-6)
=-6/(-10)
=3/5