Explanation:

Here is the solution to this problem…..
The given equations are:
a (a + b + c) = 45 …….(i)
b (a + b + c) = 75 ……..(ii)
c (a + b + c)= 105 …….(iii)
Adding (i), (ii) and (iii), we get:
(a + b + c) (a + b + c) =45 + 75 + 105
i.e. (a + b + c)^2 = 225
Taking square root on both sides of above eqn., we get:
(a + b + c) = 15
Put the value of (a + b + c) in eqn.s (i), (ii) and (iii), we get:
a × 15 = 45
b × 15 = 75
c × 15 = 105
This implies that
a = 3, b = 5, c = 7
So, we have
(a^2 + b^2 + c^2) = 3^2 + 5^2 + 7^2
= 9 + 25 + 49
=83