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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

  • question_answer
    If p and q are prime numbers satisfying the condition \[{{p}^{2}}-2{{q}^{2}}=1,\] then the value of \[{{p}^{2}}+2{{q}^{2}}\]is

    A)  \[5\]                                    

    B)  \[15\]

    C)  \[16\]                                  

    D)  \[17\]

    Correct Answer: D

    Solution :

    Given, \[{{p}^{2}}-2{{q}^{2}}=1\]                              ...(i) Since, p and q are prime numbers. Let \[p=3\]and \[q=2\] \[\therefore \]From Eq.(i),   \[{{(3)}^{2}}-2{{(2)}^{2}}=1\] \[\Rightarrow \]               \[9-8=1\] \[\Rightarrow \]               \[1=1\] Therefore, our assumption is true. Now, \[{{p}^{2}}+2{{q}^{2}}={{(3)}^{2}}+2{{(2)}^{2}}=9+8=17\]


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