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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (II)

  • question_answer
    If\[(x-a)(x-b)=1\]and \[a-b+5=0,\] then the value of \[{{(x-a)}^{3}}-\frac{1}{{{(x-a)}^{3}}}\]is

    A) \[-125\]

    B) \[1\]

    C) \[125\]

    D) \[140\]

    Correct Answer: D

    Solution :

    [d] Given,\[(x-a)(x-b)=1\] and       \[a-b+5=0\]  \[\Rightarrow \]  \[b-a=5\] Now, \[{{(x-a)}^{3}}-\frac{1}{{{(x-a)}^{3}}}\] \[={{(x-a)}^{3}}-{{(x-b)}^{3}}\] \[=[(x-a)-(x-b)]\] \[[{{(x-a)}^{2}}+{{(x-b)}^{2}}+(x-a)(x-b)]\] \[=(b-a)[{{(x-a)}^{2}}+{{(x-b)}^{2}}+1]\] \[=5[{{\{(x-a)-(x-b)\}}^{2}}]+2\,(x-a)(x-b)+1\]   \[=5\,[{{(x-a-x+b)}^{2}}+2]+1\] \[=5\,[{{(5)}^{2}}+3]=5\times 28=140\]


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