Question 1207818: Prove that if $a,$ $b,$ and $c$ are positive real numbers, then
sqrt(a^2-ab+b^2)+sqrt(a^2-ac+c^2) >= sqrt(b^2+bc+c^2)
When does equality occur?
Hint(s):
The expressions inside the radicals remind us of the Law of Cosines. Moreover, if we interpret the radicals as lengths, the inequality has the form of the Triangle Inequality.
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
In this post, I will not solve the problem.
Instead, I am going to disprove the hint.
Would this hint be consistent with the problem, then "a", "b" and "c" be
(or are expected to be) the sides of some triangle.
But then the sides "a", "b" and "c" should satisfy the triangle inequalities.
However, the problem says " . . . for any real positive "a", "b" and "c" . . .".
Thus, just from wording, I conclude that the hint is irrelevant to the problem.
Consider it as my moderate contribution to this problem.
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