Question

If a, b, c ≥ 4 are integers, not all equal, and 4 abc = (a + 3) (b + 3) (c + 3), then what is the value of a + b + c?

Answer 1

Let a, b, c > 4

=> One of a, b, c must be 4

Let a = 4

4 × 4 × bc = (7) (3 + b) (3 + c)

16 × bc = 7 (3 + b) (3 + c)

One of b, c must be 7 let b = 7

16 × 7 × c = 7 × 10 × (3 + c)

=> c = 5

Possible (a, b, c) = (4, 7, 5) and its arrange also it is unique

∴ a + b + c = 16