Triangles Are Not Always Equilateral

Algebra Level 5

What is the largest real number \(K\) (to 2 decimal places), such that for all triangles with sides \(a, b\) and \(c\), the following inequality is always true:

\[ a^2 + b^2 + c^2 \geq K \left( a^2 + \frac{ 2abc} { a+b+c } \right). \]

Note that this inequality is neither symmetric nor cyclic.

×

Problem Loading...

Note Loading...

Set Loading...