✔ 最佳答案
◎若 (x4 + 2x3 + 3x2 + 4x + 5)(5x3 + 4x2 +3x + 2) = ax7 + bx6 + cx5 + dx4 + ex3 + fx2 + gx + h,則:
(1) a + b + c + d + e + f + g + h =?
ax7 + bx6 + cx5 + dx4 + ex3 + fx2 + gx + h
= (x4 + 2x3 + 3x2 + 4x + 5)(5x3 + 4x2 +3x + 2)
令 x = 1:
a + b + c + d + e + f + g + h
= (1 + 2 + 3 + 4 + 5)(5 + 4 + 3 + 2)
= 15 x 14
= 210
(2) a - b + c - d + e - f + g - h =?
ax7 + bx6 + cx5 + dx4 + ex3 + fx2 + gx + h
= (x4 + 2x3 + 3x2 + 4x + 5)(5x3 + 4x3 +3x + 2)
令 x = -1:
-a + b - c + d - e + f - g + h
= (1 - 2 + 3 - 4 + 5)(-5 + 4 - 3 + 2)
= 3 x (-2)
= -6
所以,a - b + c - d + e - f + g - h = 6
(3) a + c + e + g =?
a + b + c + d + e + f + g + h = 210 ... (*)
a - b + c - d + e - f + g - h = 6 ... (#)
(*) + (#):
2a + 2c + 2e + 2g = 216
所以, a + c + e + g = 108
(4) b + d + f + h =?
a + b + c + d + e + f + g + h = 210 ... (*)
a - b + c - d + e - f + g - h = 6 ... (#)
(*) - (#):
2b + 2d + 2f + 2h = 204
所以, b + d + f + h = 102
◎如圖,矩形ABCD中,長AB線=3x+2,寬AD線=2x-1,若將AD線摺疊到
AB線上,使得D與F重合,則矩形BCEF面積為何?
D───E───C
| | |
|───────|
A F B
BCEF 面積
= BC x FB
= (2x - 1)[(3x + 2) - (2x - 1)]
= (2x - 1)(x + 3)
= 2x2 + 6x - x - 3)
= 2x2 + 5x - 3
2009-08-16 18:00:54 補充:
第一題:
若把乘式展開,可得:
a = 5, b = 14, c = 26, d = 40, e = 54, f = 38, g = 23, = 10
「小儀子」計算 g 時錯了,導致 (1), (2), (3) 錯了。
2009-08-16 18:04:03 補充:
To tarcor:
第一題:g = 23 (不是 14)
第二題:常數項是 -3 (不是 +3)