If {a^{1/x}} = {b^{1/y}} = {c^{1/z}} and a,;b | vedclass

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Question

(a) Let ${a^{1/x}} = {b^{1/y}} = {c^{1/z}} = k$

$\Rightarrow a = {k^x},\,b = {k^y},\;c = {k^z}$

Now, $a,\;b,\;c$are in $G.P.$

$ \Rightarrow $

Vedclass · Accepted Answer

$A.P.$

Vedclass · Answer

(a) Let ${a^{1/x}} = {b^{1/y}} = {c^{1/z}} = k$

$\Rightarrow a = {k^x},\,b = {k^y},\;c = {k^z}$

Now, $a,\;b,\;c$are in $G.P.$

$ \Rightarrow $ ${b^2} = ac $

$\Rightarrow {k^{2y}} = {k^x}.{k^z} = {k^{x + z}} $

$\Rightarrow 2y = x + z$

$ \Rightarrow $ $x,\;y,\;z$ are in $A.P.$

If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and $a,\;b,\;c$ are in $G.P.$, then $x,\;y,\;z$ will be in

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