Given a+b+c=3,
Is a^2+b^2+c^2 greater than, less than, equal to 6, or not enough information provided?
Algebra
2013-11-15 12:56 pm
回答 (3)
2013-11-15 4:00 pm
✔ 最佳答案
when a = b = c = 1, a^2 + b^2 + c^2 = 3when a = b = 2, c = -1, a^2 + b^2 + c^2 = 9
so, not enough information provided
參考: knowledge
2013-11-16 9:06 am
Not enough information is provided since a b c can be many variables if it is just given that their sum is 3.
參考: Me..
2013-11-16 4:01 am
If a+b+c=3, then a^2+b^2+c^2>=3 where a, b, c are real.
Proof:
By Schwartz inequality,
(ax1+bx1+cx1)^2<=(a^2+b^2+c^2) (1^2+1^2+1^2)
3^2<=(a^2+b^2+c^2) (3)
a^2+b^2+c^2>=3.
Proof:
By Schwartz inequality,
(ax1+bx1+cx1)^2<=(a^2+b^2+c^2) (1^2+1^2+1^2)
3^2<=(a^2+b^2+c^2) (3)
a^2+b^2+c^2>=3.
收錄日期: 2021-04-28 14:22:18
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131115000051KK00030