Solution Found!
The quadratic mean of two real numbers x and y equals By
Chapter 8, Problem 24E(choose chapter or problem)
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,