(x+2)^2-(y-3)^2=(x+y)(x-y)...( 1)
x-3y=2...(2)
X=3y+2...(3) From (2), substitute (3) into (1) to get:
(3y+4) 2-(y-3) 2 = (4y+2) (2y+2), the solution is:
y=- 1/6...(4),
Substitution into (2) gives:
x=3/2
2. 1
(X-Y)^2
=X^2+2XY+Y^2-4XY
=(X+Y)^2-4XY
=49/36-4XY
=625/36XY
=-4
So XY+4=-4+4=0.
2.2
a-b=2,b-c=-3,c-d=5
a-c=(a-b)+(b-c)=2-3=- 1
b-c=(b-c)+(c-d)=-3+5=2
a-d=(a-b)+(b-c)+(c-d)=2-3+5=4
therefore
(a-c)(b-d)/(a-d)=- 1/2