The quadratic mean of two real numbers x and y equals By

Chapter 8, Problem 24E

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QUESTION:

The quadratic mean of two real numbers \(x\) and \(y\) equals \(\sqrt{\left(x^{2}+y^{2}\right) / 2}\). By computing the arithmetic and quadratic means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.

Equation Transcription:

Text Transcription:

x

y

sqrt{(x^{2}+y^{2})/2}

Questions & Answers

QUESTION:

The quadratic mean of two real numbers \(x\) and \(y\) equals \(\sqrt{\left(x^{2}+y^{2}\right) / 2}\). By computing the arithmetic and quadratic means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.

Equation Transcription:

Text Transcription:

x

y

sqrt{(x^{2}+y^{2})/2}

ANSWER:

SOLUTION

Step 1

We have

The quadratic mean of two positive real numbers is,

Arithmetic mean is,  

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