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  5. Simplification

Railways Quantitative Aptitude Simplification Sample Paper Simplification Sample Test Paper-3

  • question_answer
    If \[a=2+\sqrt{3}\] and & \[b=2-\sqrt{3}\] then \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\] is equal to

    A)  14                   

    B)  \[-14\]    

    C)  \[8\sqrt{3}\]     

    D)  \[-8\sqrt{3}\]

    Correct Answer: A

    Solution :

    [a] \[a=2+\sqrt{3}\]                   \[b=2-\sqrt{3}\] \[{{a}^{2}}=4+4+4\sqrt{3}\]  \[{{b}^{2}}=4+3-4\sqrt{3}\] \[=7+4\sqrt{3}\]                        \[=7-4\sqrt{3}\] \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{7+4\sqrt{3}}+\frac{1}{7-4\sqrt{3}}\] \[=\frac{7-4\sqrt{3}+7+4\sqrt{3}}{49-48}\] = 14


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