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Where does the Cauchy-Schwarz inequality apply in life?  $\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$ where $a_k$ and $b_k$ are real numbers, for any $k$
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