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NTSE Sample Paper NTSE SAT Practice Test-18

  • question_answer
    If x = \[1+\sqrt{2}\]and y =\[1-\sqrt{2}\], then the value of \[({{x}^{4}}+{{y}^{4}})\]is

    A) 38        

    B)                      34

    C) \[38\sqrt{2}\]                

    D) \[36\sqrt{2}\]

    Correct Answer: B

    Solution :

    [b] \[{{x}^{2}}+{{y}^{2}}={{(x+y)}^{2}}-2xy.\]Now, \[x+y=2,\] And \[x\times y=-1\] \[\therefore \,\,{{x}^{2}}+{{y}^{2}}=22-2(-1)=6\] \[{{x}^{4}}+{{y}^{4}}={{({{x}^{2}}+{{y}^{2}})}^{2}}-2{{x}^{2}}{{y}^{2}}\] \[=36-2=34\]


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