f.4 mathz,

let the number be x and the other number be (10-x) and the sum of the squ. of these two numbers be y.
the sum of the squ.
y=x^2+(10-x)^2
y=x^2+x^2-20x+100
y=2x^2-20x+100
by completing the squ.
y=2(x^2-10x+50)
y=2(x^2-10x+5^2+50-5^2)
y=2(x-5)^2+50

so the minimum value of y is 50.
so the minimum value of the sum of the squ. of these two numbers is 50.

Let the no.s are n and (10-n)
by considering, n^2+(10-n)^2=2(n^2-10n+50)
=2(n-5)^2+50
the minimum value is 50