+0  
 
0
23
1
avatar

Let a, b, and c be positive real numbers. Prove that

 

\(\sqrt{a^2 - ab + b^2} + \sqrt{a^2 - ac + c^2} \ge \sqrt{b^2 + bc + c^2}.\)

 

Under what conditions does equality occur? That is, for what values of a, b, and c are the two sides equal?

 
 Jul 21, 2021
 #1
avatar
+1

By the Cosine Law, a^2 - ab + b^2 = c^2 cos C.  Plug in similar expressions, and the rest is easy.

 
 Jul 21, 2021

5 Online Users