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SSC Sample Paper SSC CGL - Sample Paper-15

  • question_answer
    If \[{{x}^{2}}+{{y}^{2}}+\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=4,\] then the value of \[{{x}^{2}}+{{y}^{2}}\] is

    A) 2                                 

    B) 4        

    C) 8                                 

    D) 16

    Correct Answer: A

    Solution :

    \[{{x}^{2}}+{{y}^{2}}+\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}-4=0\] \[\Rightarrow \]   \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-2+{{y}^{2}}+\frac{1}{{{y}^{2}}}-2=0\] \[\Rightarrow \]   \[{{\left( x+\frac{1}{x} \right)}^{2}}+{{\left( y+\frac{1}{y} \right)}^{2}}=0\] \[\Rightarrow \]   \[x-\frac{1}{x}=0\] \[\Rightarrow \]   \[{{x}^{2}}-1=0\] \[\Rightarrow \] \[x=1\]


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