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NTSE Sample Paper NTSE SAT Practice Test-16

  • question_answer
    If the average of x and \[{{x}^{-1}}\]is M, then what is the average of\[{{x}^{3}}\]and\[{{x}^{-3}}\]?

    A) \[\frac{M({{M}^{2}}-3)}{3}\]  

    B) \[{{M}^{3}}\]

    C) \[{{M}^{3}}-3\]                      

    D) \[M(4{{M}^{2}}-3)\]

    Correct Answer: D

    Solution :

    [d] \[x+\frac{1}{x}=2\,\,M\] Average of \[{{x}^{3}}\] and \[{{x}^{-3}}=\frac{1}{2}\left( {{x}^{3}}+\frac{1}{{{x}^{3}}} \right)\] \[=\frac{1}{2}\left[ {{\left( x+\frac{1}{x} \right)}^{3}}-3\left( x+\frac{1}{x} \right) \right]\] \[=\frac{1}{2}[8{{M}^{3}}-6M]=M(4{{M}^{2}}-3)\]


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