若(X+Y)(1-X-Y)+6=0.求X+Y的值

令L=X+Y
则L(1-L)+6=0
L²-L-6=0
(L-3)(L+2)=0
L=3或-2
既X+Y=3或-2

(X+Y)(1-X-Y)+6=0
(X+Y)[1-(X+Y)]+6=0
(X+Y)-(X+Y)^2+6=0
(X+Y)^2-(X+Y)-6=0
(X+Y-3)(X+Y+2)=0
所以X+Y-3=0或X+Y+2=0
X+Y=3或-2

设x+y=z那么原方程就相当于
z(1-z)+6=0
z=-2 or z=3

(X+Y)(1-X-Y)+6=0
(X+Y)<1-(X+Y)>+6=0
设x+y为A 则上式可写为
A(1-A)=-6
A^2-A+6=0
(A-3)(A=2)=0
得A1=3,A2=-2
所以X+Y的值为3 或-2