Prove the inequality?
回答 (1)
2021-04-18 5:52 pm
✔ 最佳答案
Let a = mc and b = nc.a^2 + b^2 + c^2 - c(a + b)
= (m^2 + n^2 + 1)c^2 - c^2(m + n)
= c^2(m^2 + n^2 - m - n + 1)
= c^2((m - 1/2)^2 + (n - 1/2)^2 + 1/2)
c^2 is non-negative and (m - 1/2)^2 + (n - 1/2)^2 + 1/2 is positive,
so a^2 + b^2 + c^2 - c(a + b) is non-negative.
Therefore, a^2 + b^2 + c^2 ≧ c(a + b).
收錄日期: 2021-04-24 08:49:57
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20210418084823AA2oaQy