已知a, b, c分別是一個三角形的三邊長，若a, b, c符合以下條件，試判斷它的形狀(等腰三角形、等邊三角形、直角三角形、等腰直角三角形等)。
a^2 + b^2 + c^2 – 13790a – 13788b – 13790c + 142609286 = 0
數學問題集(12)---三角形的形狀---II
2010-08-24 2:27 am
回答 (1)
2010-08-24 3:33 am
✔ 最佳答案
a^2 + b^2 + c^2 – 13790a – 13788b – 13790c + 142609286 = 0(a^2 - 13790a + 47541025)+(c^2 - 13790c + 47541025) + (b^2 - 13788b + 47527236) = 0
(a-6895)^2 + (b-6894)^2 + (c-6895)^2 = 0
Since (a-6895)^2 , (b-6894)^2, (c-6895)^2 are all >= 0,
Hence, a = 6895, b = 6894, c = 6895
Therefore, It's an isosceles triangle.
參考: Hope the soluton can help you^^”
收錄日期: 2021-04-13 17:27:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100823000051KK01520