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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-21

  • question_answer
    If \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}=0,\] then \[{{a}^{9}}-{{b}^{9}}-{{c}^{9}}-3{{a}^{3}}{{b}^{3}}{{c}^{3}}=?\]

    A)  1

    B)  2

    C)  0

    D)  3

    Correct Answer: C

    Solution :

     \[{{a}^{3}}-{{b}^{3}}-{{c}^{3}}=0,\] \[\therefore \,\,\,{{a}^{3}}-{{b}^{3}}={{c}^{3}}\] Taking cube of both side: \[{{({{a}^{3}}-{{b}^{3}})}^{3}}={{({{c}^{3}})}^{3}}\Rightarrow {{a}^{9}}-{{b}^{9}}-3{{a}^{3}}{{b}^{3}}({{a}^{3}}-{{b}^{3}})={{c}^{9}}\] \[{{a}^{9}}-{{b}^{9}}-3{{a}^{3}}{{b}^{3}}{{c}^{3}}={{c}^{9}}\] \[{{a}^{9}}-{{b}^{9}}-{{c}^{9}}-3{{a}^{3}}{{b}^{3}}{{c}^{3}}=\underline{\mathbf{0}}\]


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