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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    If\[x,y,z\]are in AP, then \[\frac{1}{\sqrt{x}+\sqrt{y}},\frac{1}{\sqrt{z}+\sqrt{x}},\] \[\frac{1}{\sqrt{y}+\sqrt{z}}\] are in:

    A)  AP

    B)                                         GP

    C)  HP                        

    D)         AP and HP

    E)  AP and GP

    Correct Answer: A

    Solution :

    \[\because \] \[\frac{1}{\sqrt{z}+\sqrt{x}}-\frac{1}{\sqrt{x}+\sqrt{y}}\] \[=\frac{1}{\sqrt{y}+\sqrt{z}}-\frac{1}{\sqrt{z}+\sqrt{x}}\] \[\Rightarrow \]               \[y-z=x-y\] \[\Rightarrow \]               \[y=\frac{z+x}{2}\] \[\Rightarrow \]               \[x,\text{ }y,\text{ }z\]are in AP Hence, \[\frac{1}{\sqrt{x}+\sqrt{y}},\frac{1}{\sqrt{z}+\sqrt{x}},\frac{1}{\sqrt{y}+\sqrt{z}}\] are in AP.


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