Question

Ten non-negative numbers are such that their sum is 3, and the sum of their squares is 5.8. What is the greatest value of the largest of these numbers?

Answer 1

In this problem,

a₁+a₂+a₃+a₄+a₅+a₆+a₇+a₈+a₉+a₁₀=3

a₁²+a₂²+a₃²+a₄²+a₅²+a₆²+a₇²+a₈²+a₉²+a₁₀²=5.8. It is clear that all numbers are non-negative and they are not integer numbers. In this case, we have ten unknowns and we have also only two equations to find unknowns. I can say that it is impossible to find not only the greatest but also unknowns.