Final answer:
The problem involves finding three numbers that minimize the sum of their squares, which is an optimization problem within Mathematics.
Step-by-step explanation:
The question asks for three numbers whose sum is known and whose sum of squares is a minimum. The minimization of a function concerning its variables, in this case, the sum of squares of the numbers, is a problem best addressed using optimization techniques. To find the numbers, you'd typically employ calculus to take derivatives and find where they are zero to identify local minima.
The information provided, such as examples of linear equations and quadratic equations, suggests that the optimization process might involve concepts from these areas, but specifically, it is an optimization problem. Hence, the correct subject is Mathematics, and the appropriate topic area is optimization, making the correct option c) Optimization.