The A.M., G.M. and H.M. between two numbers a | vedclass

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Question

(B) For any two positive numbers,the relationship between Arithmetic Mean $(A.M.)$,Geometric Mean $(G.M.)$,and Harmonic Mean $(H.M.)$ is given by the

Vedclass · Accepted Answer

$\frac{144}{15}, 12, 15$

Vedclass · Answer

(B) For any two positive numbers,the relationship between Arithmetic Mean $(A.M.)$,Geometric Mean $(G.M.)$,and Harmonic Mean $(H.M.)$ is given by the inequality $A.M. \ge G.M. \ge H.M.$Given values are $\frac{144}{15} = 9.6$,$15$,and $12$.Comparing these values,we have $15 > 12 > 9.6$.Therefore,$A.M. = 15$,$G.M. = 12$,and $H.M. = \frac{144}{15}$.We are asked to find the values in the order $H.M., G.M., A.M.$Substituting the identified values,we get $\frac{144}{15}, 12, 15$.

The $A.M., G.M.$ and $H.M.$ between two numbers are $\frac{144}{15}$,$15$ and $12$,but not necessarily in this order. Then $H.M., G.M.$ and $A.M.$ respectively are

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