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

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

Advanced Engineering Mathematics
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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(a) Recall that > 0 for every positive real number r. Prove that if a and b are positive real numbers, then 0 < Jab < b. (The number Jab 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 Vab = (a +b)/2 for positive real numbers a and b? Justify your answer.
Transcribed Image Text:(a) Recall that > 0 for every positive real number r. Prove that if a and b are positive real numbers, then 0 < Jab < b. (The number Jab 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 Vab = (a +b)/2 for positive real numbers a and b? Justify your answer.
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