- #1
fabbi007
- 20
- 0
Homework Statement
[itex]
d(x,y)=(a|x_1-y_1|^2+b|x_1-y_1||x_2-y_2|+c|x_2-y_2|^2)^{1/2}
[/itex]
where [itex]a>0, b>0, c>0[/itex] and [itex]4ac-b^2<0[/itex]
Show whether [itex]d(x,y)[/itex] exhibits Triangle inequality?
Homework Equations
(M4) [itex] d(x,y) \leq d(x,z)+d(z,y) [/itex] (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.
[itex] d^2(x,y); [d(x,z)+d(z,y)]^2. [/itex] 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?