If alpha, beta, gamma are the geometric means | vedclass

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(A) Given that $\alpha, \beta, \gamma$ are geometric means between $(ca, ab), (ab, bc), (bc, ca)$ respectively.Therefore,$\alpha^2 = (ca)(ab) = a^2bc$

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$A.P.$

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(A) Given that $\alpha, \beta, \gamma$ are geometric means between $(ca, ab), (ab, bc), (bc, ca)$ respectively.Therefore,$\alpha^2 = (ca)(ab) = a^2bc$,$\beta^2 = (ab)(bc) = ab^2c$,and $\gamma^2 = (bc)(ca) = abc^2$.Since $a, b, c$ are in $A.P.$,we have $2b = a + c$.We want to check the progression of $\alpha^2, \beta^2, \gamma^2$,which are $a^2bc, ab^2c, abc^2$.Dividing each term by $abc$,we get $a, b, c$.Since $a, b, c$ are in $A.P.$,it follows that $a^2bc, ab^2c, abc^2$ are also in $A.P.$ because they are obtained by multiplying each term of the $A.P.$ by the constant $abc$.

If $\alpha, \beta, \gamma$ are the geometric means between $ca, ab$; $ab, bc$; and $bc, ca$ respectively,where $a, b, c$ are in $A.P.$,then $\alpha^2, \beta^2, \gamma^2$ are in

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