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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-4

  • question_answer
    \[\frac{{{({{a}^{2}}-{{b}^{2}})}^{3}}+{{({{b}^{2}}-{{c}^{2}})}^{3}}+{{({{c}^{2}}-{{a}^{2}})}^{3}}}{{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{3}}}=?\]

    A) \[3(a-b)(b-c)(c-a)\]          

    B) \[3(a+b)(b+c)(c+a)\]  

    C) \[(b-a)(b-c)(c-a)\]

    D) \[(a+b)(b+c)(c+a)\]

    Correct Answer: B

    Solution :

     If\[a+b+c=0\]             \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] Here,     \[{{a}^{2}}-{{b}^{2}}+{{b}^{2}}-{{c}^{2}}+{{c}^{2}}-{{a}^{2}}=0\] and       \[a-b+b-c+c-a=0\] \[\therefore \]Expression             \[=\frac{3({{a}^{2}}-{{b}^{2}})({{b}^{2}}-{{c}^{2}})({{c}^{2}}-{{a}^{2}})}{(a-b)(b-c)(c-a)}\]             \[=2(a+b)(b+c)(c+a)\]


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