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.

"> 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.

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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       [IIT 1969; UPSEAT 2001]

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) . 9 months ago

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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.

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Posted on 06 Sep 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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