(1)已知a,b满足a
2+b
2+4a-8b+20=0,试分解(x
2+y
2)-(b+axy);
(2)计算:(1-
)(1-
)(1-
)…(1-
)(1-
);
(3)设a=1999x+1998,b=1999x+1999,c=1999x+2000,求a
2+b
2+c
2-ab-ac-bc的值.
(1)a2+b2+4a-8b+20=0,(a+2)2+(b-4)2=0,所以a=-2,b=4,(x2+y2)-(4-2xy)=x2+y2+2xy-4=(x+y)2-4=(x+y+2)(x+y-2);(2)原式=(1-12)×(1+12)×(1-13)×(1+13)×(1-14)×(1+14)×…×(1-...