Question

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Stats. pg15.20 Ex. 15.1.19:
Given two positive numbers a and b. prove that AH=G^2. Does the result hold for any set of observations?

explain in detail step by step

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Answer 1

Answer:

Given that a and b are two positive numbers :

A.M = $\dfrac{a+b}{2}$

G.M = $\sqrt{ab}$

H.M = $\dfrac{2ab}{a+b}$

$A.M\times H.M =\dfrac{a+b}{2}\times \dfrac{2ab}{a+b}\\\\\implies ab\\\\\implies (G.M)^2$

The result will hold true for any two positive numbers only .

The result must not have any negative number .

From the relation we can also get the A.M - G.M inequality .

Answer 2

Answer:

i hope it will help ..........