Question

解方程组(x+2)(x-2)=xy并且√(x+1)(y+4)+x+3=0

Answer 1

解方程组(x+2)(x-2)=xy并且√(x+1)(y+4)+x+3=0
(x+2)(x-2)=xy
x^2-4=xy
√(x+1)(y+4)+x+3=0
√(x+1)(y+4)=-(x+3)
则有x+3<=0即x<=-3
(x+1)(y+4)=(x+3)^2
xy+4x+y+4=x^2+6x+9
x^2-4+4x+y+4=x^2+6x+9
y=2x+9
x^2-4=x(2x+9)
x^2-4=2x^2+9x
x^2+9x+4=0
x=(-9±√9^2-4*1*4)/2
x=(-9±√65)/2
因为x<=-3
即x=(-9-√65)/2
y=2*(-9-√65)/2+9
y=-√65

Answer 2

1xy=x²-4
则√﹙x＋1﹚﹙y＋4﹚=√x²＋y＋4x
则﹙－x－3﹚²=x²＋y＋4x
则y=2x＋9
代入得x=-9/2-(√65)/2
y=-√652解方程组(x+2)(x-2)=xy并且√(x+1)(y+4)+x+3=0
(x+2)(x-2)=xy
x^2-4=xy
√(x+1)(y+4)+x+3=0
√(x+1)(y+4)=-(x+3)
则有x+3<=0即x<=-3
(x+1)(y+4)=(x+3)^2
xy+4x+y+4=x^2+6x+9
x^2-4+4x+y+4=x^2+6x+9
y=2x+9
x^2-4=x(2x+9)
x^2-4=2x^2+9x
x^2+9x+4=0
x=(-9±√9^2-4*1*4)/2
x=(-9±√65)/2
因为x<=-3
即x=(-9-√65)/2
y=2*(-9-√65)/2+9
y=-√65
好评偶

Answer 3

x=-9/2-(√65)/2
y=-√65

追问

步骤。。

追答

x^2 - 4 == x y①
√(x+1)(y+4)=-(x+3)
(1 + x) (4 + y) == (3 + x)^2
4 + 4 x + y + x y == 9 + 6 x + x^2
①代入上式
4+4x+y+x^2-4==9+6x+x^2
2x-y+9==0
y=9+2x
代入①
x^2-4==x(9+2x)
x1 = 1/2 (-9 - √65),x2 = 1/2 (-9 + √65)
y1=-√65,y2=√65
验算:
当x=1/2 (-9 + √65) ,y=√65
√(x+1)(y+4)+x+3≠0
舍去
∴
x=-9/2-(√65)/2
y=-√65