Maths

Let two number are x,10-x.
x2+(10-x)^2
=x2+(100-20x+x2)
=2x2-20x+100
=2(x2-10x)+100
=2(x2-10x+25)+100-50
=2(x-5)2+50
∴ the sum of their squares is a minimum=50

The sum of two positives that is 10:

1, 9
2 , 8
3 , 7
4 , 6
5 , 5


the sum of their squares:

82
68
58
52
50<


since 50 is the minimum;

therefore the two positives are 5 & 5.