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Brute force and maximal ignorance mode:

0+14=14 0²+14²=196
1+13=14 1²+13²=170
2+12=14 2²+12²=148
3+11=14 3²+11²=130
4+10=14 4²+10²=116
5+9=14 5²+9²=106
6+8=14 6²+8²=100
7+7=14 7²+7²=98
8+6=14 8²+6²=100
9+5=14 9²+5²=106
10+4=14 10²+4²=116
11+3=14 11²+3²=130
12+2=14 12²+2²=148
13+1=14 13²+1²=170
14+0=14 14²+0²=196

Thus, the minimum is at both numbers being 7.

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Q: Find two positive numbers whose sum is 14 and the sumof whose square is minimum?
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