Question

Problem: What values of a and b make this statement false? |a-b|=|a|-|b|

Answer 1

All (a,b) that satisfy a.b < 0 will make that statement false

Explanation:

It is only right when:

|a-b| = |a| - |b|

<=> ( |a-b| ) ^ 2 = ( |a| - |b| ) ^ 2

<=> a^2 - 2ab + b^2 = a^2 - 2.|ab| + b^2

<=> ab = |ab|

<=> ab ≥ 0

So, when ab < 0, it's wrong