1) Consider the arithmetic mean (x +y)/2 and the geometric mean xy of two positive numbers x and y. a) compute their values for x = 2, y = 8. And for x = 3 = 3. b) conjecture how they compare in general. Give quantified assertion over N. c) prove your conjecture. Hint: chain of iff's to (x – y)2 20
1) Consider the arithmetic mean (x +y)/2 and the geometric mean xy of two positive numbers x and y. a) compute their values for x = 2, y = 8. And for x = 3 = 3. b) conjecture how they compare in general. Give quantified assertion over N. c) prove your conjecture. Hint: chain of iff's to (x – y)2 20
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:**Arithmetic and Geometric Means**
1) Consider the arithmetic mean \((x + y)/2\) and the geometric mean \(\sqrt{xy}\) of two positive numbers \(x\) and \(y\).
a) Compute their values for \(x = 2, y = 8\). And for \(x = 3 = 3\).
b) Conjecture how they compare in general. Give quantified assertion over \(\mathbb{N}\).
c) Prove your conjecture. Hint: chain of iff's to \((x - y)^2 \geq 0\).
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