把一條長24m的鐵線剪成兩段。然後把所得的兩段鐵線分別屈成兩個正方形。
以X表示兩個正方形的總面積A。
24m
----------------------------------
↓
Xm
-----------
(24-x)m
----------------------
只知答案是：
(x-12)^2+18
__________
8
請各位幫幫忙
f.4 maths
2006-10-16 2:53 am
回答 (4)
2006-10-16 3:08 am
✔ 最佳答案
length 1 = xlength 2 = 24 - x
side 1 = x/4
side 2 = (24-x)/4
area of square = L^2
so total are = (x/4)^2 + [(24-x)/4]^2
= (x/4)^2 + [6-(x/4)]^2
= (x/4)^2 + 36 - 3x +(x/4)^2
= 2(x^2/16) - 3x +36
= x^2/8 -3x +36
= 1/8 (x^2 -24x + 288)
use completing of square
=1/8(x^2 - 24x +144 + 144)
=1/8(x-12)^2 +144/8
=1/8(x-12)^2 +18
2006-10-16 3:15 am
A
= (x/4)^2 + [(24-x)/4]^2
= x^2/16 +(576-48x+x^2)/16
= (2x^2 -48x + 576)/16
= (x^2 - 24x + 288)/8
= (x/4)^2 + [(24-x)/4]^2
= x^2/16 +(576-48x+x^2)/16
= (2x^2 -48x + 576)/16
= (x^2 - 24x + 288)/8
2006-10-16 3:09 am
A = (X/4)^2 + (24-X/4)^2
= X^2/16 + (576-48X+X^2)/16
= (2X^2-48X+576)/16
= X^2/8-3X+36
= 1/8(X^2-24X)+36
= 1/8(X-12)^2=18
2006-10-15 19:10:06 補充：
最尾打錯左，係咁sin岩:=1/8(X-12)^2+18
= X^2/16 + (576-48X+X^2)/16
= (2X^2-48X+576)/16
= X^2/8-3X+36
= 1/8(X^2-24X)+36
= 1/8(X-12)^2=18
2006-10-15 19:10:06 補充：
最尾打錯左，係咁sin岩:=1/8(X-12)^2+18
2006-10-16 3:03 am
我計到:
(x/4)^2 + ((24-x)/4)^2 全長除4即係一個正方形既邊
=(x/4)^2 + (6-x/4)^2
=x^2/16 + 24 - 3x + x^2/16
=x^2/8 - 3x +24
(x/4)^2 + ((24-x)/4)^2 全長除4即係一個正方形既邊
=(x/4)^2 + (6-x/4)^2
=x^2/16 + 24 - 3x + x^2/16
=x^2/8 - 3x +24
收錄日期: 2021-04-25 18:30:02
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061015000051KK04919