Explanation:
Using | a – b | ≥ | c |, we obtain |a – b|2 ≥ |c|2, which is equivalent to (a – b – c)(a – b + c) ≥ 0. Similarly, (b – c – a) (b – c + a) ≥ 0 and (c – a – b) (c – a + b) ≥ 0 .Multiplying these inequalities, We get
- (a + b – c)2 (b + c – a)2 (c +a-b)2 ≥ 0.
This forces that LHS is equal to zero. Hence it follows that either a + b = c, or b + c = a, or c + a = b