An Interesting Inequality

Algebra Level pending

Say that for 'n' real numbers, \({ x }_{ 1 },{ x }_{ 2 },...,{ x }_{ n }\), the smallest number is 'a', and the largest number is 'b'. If \(\sum _{ i=1 }^{ n }{ { x }_{ i } } =0\quad and\quad \sum _{ i=1 }^{ n }{ { { x }_{ i } }^{ 2 } } =1\), then \(ab\le y\). What is 'y' in terms of 'n'?

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