Suppose the difference of two numbers is 3. Does the sum of their squares have a minimum or maximum value? What is that value?
let the first number be x
and let the second number be x+3
sum of squares = x^2 + (x+3)^2
= 2x^2 + 6x + 9
which is a quadratic whose graph opens upwards
Thus we have a minimum , which is the vertex.
Since you labeled your post as "Precalc" I will not use Calculus.
the x of the vertex is -b/(2a) = -6/4 = -3/2
yielding a value of
(-3/2)^2 + (-3/2 + 3)^2 = 477/16 or 29.8125