Linear Algebra Done Right · Problem 6A.12

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · inner-products-and-norms

Problem

Suppose a,b,c,da, b, c, d are positive numbers. ((a)) Prove that (a+b+c+d)(1a+1b+1c+1d)≥16(a + b + c + d)\left(\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} + \dfrac{1}{d}\right) \geq 16. ((b)) For which positive numbers a,b,c,da, b, c, d is the inequality above an equality?

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