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NTSE Sample Paper NTSE SAT Practice Test-7

  • question_answer
    If \[x+y=\sqrt{3}\] and \[x-y=\sqrt{2}\], then the value of \[8xy({{x}^{2}}+{{y}^{2}})\]

    A) \[5\sqrt{2}\]                  

    B) \[10\sqrt{2}\]

    C) 20                                

    D) 5

    Correct Answer: D

    Solution :

    [d] \[{{\left( x+y \right)}^{2}}+{{\left( x-y \right)}^{2}}=2\left( {{x}^{2}}+{{y}^{2}} \right)\text{ }and\text{ }{{\left( x+y \right)}^{2}}\] \[-{{\left( x-y \right)}^{2}}=4xy\] \[=\left[ {{(\sqrt{3})}^{2}}+{{(\sqrt{2})}^{2}} \right]\times \left[ {{(\sqrt{3})}^{2}}-{{(\sqrt{2})}^{2}} \right]\] \[=5\times 1=5\]


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