.①（x+y）（-x-y）=-(x+y)(x+y)=-x2-y2-2xy
②a²+b²-8a-10b+41=0
a²-8a+16+b²-10b+25=0
(a-4)2+(b-5)2=0
a=4 b=5
5a-b²+25=20
③x²y²+x²+y²+1=4xy
x²y²+x²+y²+1-4xy=0
x²y²-2xy+1+x²+y²-2xy=0
(xy-1)2+(x-y)2=0
xy=1 x=y
x²=1 x=y=1或-1
2x+y-1=3x-1=2或-4
④a=1/3x+2006,b=1/3x+2007,c=1/3x+2008
則a-b=-1 a-c=-2 b-c=-1
a²+b²+c²-ab-ac-bc=1/2 (2a²+2b²+2c²-2ab-2ac-2bc)
=1/2((a-b)2+(b-c)2+(a-c)2 )=1/2(1+1+4)=3
⑤提示x²-4x+1=0 x²-4x+4-3=0 (x-2)2=3 再求出x就行了最后代入求值