If the A.M.,G.M.,and H.M. between two positiv | vedclass

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(A) Given that $A.M. = G.M. = H.M.$We know that for any two positive numbers $a$ and $b$,the relationship between Arithmetic Mean $(A.M.)$,Geometric M

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$a = b$

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(A) Given that $A.M. = G.M. = H.M.$We know that for any two positive numbers $a$ and $b$,the relationship between Arithmetic Mean $(A.M.)$,Geometric Mean $(G.M.)$,and Harmonic Mean $(H.M.)$ is given by $A.M. \ge G.M. \ge H.M.$Equality holds if and only if $a = b$.Alternatively,from $A.M. = G.M.$,we have $\frac{a+b}{2} = \sqrt{ab}$.Squaring both sides,we get $\frac{(a+b)^2}{4} = ab$,which implies $(a+b)^2 = 4ab$.$(a+b)^2 - 4ab = 0$,which simplifies to $(a-b)^2 = 0$.Therefore,$a - b = 0$,or $a = b$.

If the $A.M.$,$G.M.$,and $H.M.$ between two positive numbers $a$ and $b$ are equal,then

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