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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[x={{a}^{\frac{1}{2}}}+{{a}^{\frac{1}{2}}},\]\[y={{a}^{\frac{1}{2}}}-{{a}^{\frac{1}{2}}},\]then value of \[({{x}^{4}}-{{x}^{2}}{{y}^{2}}-1)+({{y}^{4}}-{{x}^{2}}{{y}^{2}}+1)\] [SSC CGL Tier II, 2015)

    A) 12

    B) 16

    C) 14

    D) 13

    Correct Answer: B

    Solution :

    [b] \[({{x}^{4}}-{{x}^{2}}{{y}^{2}}-1)+({{y}^{4}}-{{x}^{2}}{{y}^{2}}+1)\] \[={{x}^{4}}+{{y}^{4}}-2{{x}^{2}}{{y}^{2}}={{({{x}^{2}}-{{y}^{2}})}^{2}}={{\{(x+y)(x-y)\}}^{2}}\] \[={{\{({{a}^{1/2}}+{{a}^{-1/2}}+{{a}^{1/2}}-{{a}^{-1/2}})({{a}^{1/2}}+{{a}^{-1/2}}-{{a}^{1/2}}+{{a}^{-1/2}})\}}^{2}}\]           \[={{(2{{a}^{1/2}}\times 2{{a}^{-1/2}})}^{2}}={{(4)}^{2}}=16\]


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