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NTSE Sample Paper NTSE SAT Practice Test-15

  • question_answer
                 Find the value of \[{{x}^{3}}+{{y}^{3}}\]if \[x=3\sqrt{8}\]and  \[y=3-\sqrt{8}\]       

    A) 207                              

    B) 198       

    C)       199                              

    D) 208     

    Correct Answer: B

    Solution :

    [b] \[x+y=6\text{ }and\text{ }xy=1\] \[\therefore \,\,{{x}^{3}}+{{y}^{-3}}=\frac{1}{{{x}^{3}}}+\frac{1}{{{y}^{3}}}=\frac{{{x}^{3}}+{{y}^{3}}}{{{(xy)}^{3}}}\] \[{{x}^{3}}+{{y}^{3}}={{(x+y)}^{3}}-3xy(x+y)\] \[={{6}^{3}}-3.1.6=198\] \[\therefore \,{{x}^{-3}}+{{y}^{-3}}=\frac{198}{1}=198.\]            


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