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. Prove that for any two nonnegative real numbers, their arithmetic mean is always greater than or equal to their geometric mean. Meaning, prove that for any x, y ER where x, y ≥ 0, x + y 2 Moreover, prove that there is equality if and only if x = y. > √xy.

. Prove that for any two nonnegative real numbers, their arithmetic mean is always greater than or equal to their geometric mean. Meaning, prove that for any x, y ER where x, y ≥ 0, x + y 2 Moreover, prove that there is equality if and only if x = y. > √xy.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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5. Prove that for any two nonnegative real numbers, their arithmetic mean is always greater than or equal to their geometric mean. Meaning, prove that for any x,y ER where x, y ≥ 0, x + y 2 Moreover, prove that there is equality if and only if x = y. ≥ √xy.
Transcribed Image Text:5. Prove that for any two nonnegative real numbers, their arithmetic mean is always greater than or equal to their geometric mean. Meaning, prove that for any x,y ER where x, y ≥ 0, x + y 2 Moreover, prove that there is equality if and only if x = y. ≥ √xy.
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