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NTSE Sample Paper NTSE SAT Practice Test-14

  • question_answer
    Find the value of \[{{a}^{3}}+\frac{1}{{{a}^{3}}}\]if \[2a+\frac{2}{a}=5\]    

    A) \[\frac{65}{8}\]     

    B)        8

    C) \[7\frac{5}{8}\]                         

    D) \[9\frac{3}{4}\]

    Correct Answer: A

    Solution :

    [a] \[a+\frac{1}{a}=\frac{5}{2}\] \[\Rightarrow \,{{a}^{3}}+\frac{1}{{{a}^{3}}}={{\left( a+\frac{1}{a} \right)}^{3}}-3\left( a+\frac{1}{a} \right)\] \[=\frac{125}{8}-3\times \frac{5}{2}=\frac{65}{8}.\]                 


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