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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[{{a}^{4}}+{{b}^{4}}={{a}^{2}}{{b}^{2}},\]then \[({{a}^{6}}+{{b}^{6}})\]equals to

    A) \[0\]

    B) \[-1\]

    C) \[{{a}^{2}}+{{b}^{2}}\]

    D) \[{{a}^{2}}{{b}^{4}}+{{a}^{4}}{{b}^{2}}\]

    Correct Answer: A

    Solution :

    [a] \[\because \]  \[{{A}^{3}}+{{B}^{2}}=(A+B)({{A}^{2}}+{{B}^{2}}-AB)\] On putting \[A={{a}^{2}}\]and \[B={{b}^{2}},\]we get\[({{a}^{6}}+{{b}^{6}})\] \[=({{a}^{2}}+{{b}^{2}})({{a}^{4}}+{{b}^{4}}-{{a}^{2}}{{b}^{2}})\] \[=({{a}^{2}}+{{b}^{2}})({{a}^{2}}{{b}^{2}}-{{a}^{2}}{{b}^{2}})\] \[=({{a}^{2}}+{{b}^{2}})\times 0=0\]


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