The Cauchy-Schwarz Inequality u v u v isequivalent to the inequality we get by squaring

Chapter 1, Problem 1.2.71

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The Cauchy-Schwarz Inequality u v u v isequivalent to the inequality we get by squaring bothsides: (u v)2 u2 v2.(a) In 2, with and ,this becomesProve this algebraically. [Hint: Subtract the left-handside from the right-hand side and show that thedifference must necessarily be nonnegative.](b) Prove the analogue of (a) in 3

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