Find the number of positive integral solutions for a,b,c such that a.b.c = 45?

Question

Give positive numbers a, b and c are such that
ab + bc + ca + abc = 4,
What is the value of
1/a+2 + 1/b+2 + 1/c+2 = ?

Answer 1

9,5,1
9×5×1=45

Answer 2

45 = 3 × 3 × 5
So there are 12 solutions for a, b, & c
1. 3,3,5
2. 5,3,3
3. 3,5,3
4. 1,9,5
5. 5,9,1
6. 9,5,1
7. 9,1,5
8. 1,5,9
9. 5,1,9.
10. 1,1,9
11. 1,9,1
12. 9,1,1.