Problem: a, b, c are lengths of side of a triangle

Let a, b, c are lengths of three sides of a triangle, and:

Show that: P < 0

Solution:

We can assume that c this the longest side of the triangle ABC (it does not make different if the longest side is a or b), draw the height CH with H is on AB => H is lying between points A and B (see the pic below)

then: 

let change the expression P as following: