The figure shows a right-angled triangle ABC with AB = ( x - 2 ) cm, BC = ( x + 5 ) cm and CA = ( 2x - 1 ) cm. Find the possible value( s ) of x.
我計到個x係7or-2
但點解答案會爭係寫7既?
佢個個係possible value( s ) 9係postitve number喎.
F.4 maths題目
2010-01-08 2:14 am
回答 (2)
2010-01-08 2:24 am
✔ 最佳答案
AB^2 + BC^2 = CA^2(x-2)^2 + (x+5)^2 = (2x-1)^2
x^2 - 4x + 4 + x^2 + 10x + 25 = 4x^2 - 4x + 1
2x^2 + 6x + 29 = 4x^2 - 4x + 1
2x^2 - 10x - 28 = 0
x^2 - 5x - 14 = 0
(x + 2)(x - 7) = 0
x = - 2 (rejected since AB = x-2 = -2-2 = - 4 is not possible)
or x = 7
AB = 7 - 2 = 5
BC = 7 + 5 = 12
CA = 2*7 - 1 = 13
5^2 + 12^2 = 13^2
2010-01-07 18:42:15 補充：
AB>0 , x - 2 > 0 => x > 2
BC>0 , x + 5 > 0 => x > - 5
CA>0 , 2x - 1 > 0 => x > 1/2
Combine the result above , x > 2 , so x = - 2 must be rejected.
2010-01-08 2:32 am
佢問題係問緊一幅圖..
d長度有冇可能係負數先...
你要搞清楚呢一點
先可以reject邊d roots 取邊個roots
d長度有冇可能係負數先...
你要搞清楚呢一點
先可以reject邊d roots 取邊個roots
收錄日期: 2021-04-21 22:06:41
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https://hk.answers.yahoo.com/question/index?qid=20100107000051KK01019