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Question Number 195569 by York12 last updated on 05/Aug/23

a_{i}, b_{i}, x_{i} b e r e a l s f o r i = 1, 2, 3, \dots, n, s u c h t h a t

\sum_{i = 1}^{n} [a_{i} x_{i}] = 0 . P r o v e t h a t

(\underset{i = 1}{\sum^{n}} [x_{i}^{2}]) (\underset{i = 1}{\sum^{n}} [a_{i}^{2}] \underset{i = 1}{\sum^{n}} [b_{i}^{2}] - {(\underset{i = 1}{\sum^{n}} [a_{i} b_{i}])}^{2}) ⩾ (\underset{i = 1}{\sum^{n}} [a_{i}^{2}]) {(\underset{i = 1}{\sum^{n}} [b_{i} x_{i}])}^{2}