题干
如图，已知△ABC的面积S△ABC=1.
在图（1）中，若
=
=
=
, 则S△A1B1C1=
;
在图（2）中，若
=
=
=
, 则S△A2B2C2=
;
在图（3）中，若
=
=
=
, 则S△A3B3C3=
;
按此规律，若
=
=
=
, 则S△A4B4C4=
若
=
=
=
, 则S△A8B8C8= .
在图（1）中，若
| A |
| A |
| 1 |
| A |
| B |
| B |
| B |
| 1 |
| B |
| C |
| C |
| C |
| 1 |
| C |
| A |
| 1 |
| 2 |
| 1 |
| 4 |
在图（2）中，若
| A |
| A |
| 2 |
| A |
| B |
| B |
| B |
| 2 |
| B |
| C |
| C |
| C |
| 2 |
| C |
| A |
| 1 |
| 3 |
| 1 |
| 3 |
在图（3）中，若
| A |
| A |
| 3 |
| A |
| B |
| B |
| B |
| 3 |
| B |
| C |
| C |
| C |
| 3 |
| C |
| A |
| 1 |
| 4 |
| 7 |
按此规律，若
| A |
| A |
| 4 |
| A |
| B |
| B |
| B |
| 4 |
| B |
| C |
| C |
| C |
| 4 |
| C |
| A |
| 1 |
| 5 |
若
| A |
| A |
| 8 |
| A |
| B |
| B |
| B |
| 8 |
| B |
| C |
| C |
| C |
| 8 |
| C |
| A |
| 1 |
| 9 |
答案(点此获取答案解析）
设函数关系为S=ax2+bx+c，
∵若