Thread: Triangle Inequality and Pseudometric

The problem statement, all variables and given/known data



where a>0, b>0, c>0 and

Show whether exhibits Triangle inequality?

Relevant equations:

(M4) (for all x,y and z in X)

The attempt at a solution

I started my solution by solving by squaring the both sides of the equation separately.



I am tending to think it does not satisfy the triangle inequality any other simple way to prove it? Also is this a pseudometric? if it does not satisfy the triangle inequality?

Any help is greatly appreciated!