(a) Recall that √√r> 0 for every positive real number r. Prove that if a and b are positive real numbers, then 0 <√ab atb. (The number √ab is called the geometric mean of a and b, while (a + b)/2 is ≤ called the arithmetic mean or average of a and b.) (b) Under what conditions does √ab = (a + b)/2 for positive real numbers a and b? Justify your answer.

(a) Recall that √√r> 0 for every positive real number r. Prove that if a and b are positive real numbers, then 0 <√ab atb. (The number √ab is called the geometric mean of a and b, while (a + b)/2 is ≤ called the arithmetic mean or average of a and b.) (b) Under what conditions does √ab = (a + b)/2 for positive real numbers a and b? Justify your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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