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Exercise 6.A.11

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Proof. Let $u = (\sqrt{a}, \sqrt{b}, \sqrt{c}, \sqrt{d})$ and $v = (\frac{1}{\sqrt{a}}, \frac{1}{\sqrt{b}}, \frac{1}{\sqrt{c}}, \frac{1}{\sqrt{d}})$ . Then, by 6.15, we have

4 = | ⟨ u, v ⟩ | \leq | | u | | | | v | | = \sqrt{a + b + c + d} \sqrt{\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}} .

Taking the square of each side now gives the desired result. □

celiopassos

2017-10-06 00:00

Exercise 6.A.11

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