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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[a=1,\]\[b=2\]and \[c=-\,3,\]then the value of\[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{ab+bc+ca-({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}\]is

    A) 3

    B) 2

    C) 0

    D) 1

    Correct Answer: C

    Solution :

    [c] \[a=1,\]\[b=2\]and \[c=-\,3\] Now, when a + b + c = 0 \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] Here, \[a+b+c=(1+2-3)=0\] \[\therefore \]      \[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{ab+bc+ca-({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}\] \[=\frac{3abc-3abc}{ab+bc+ca-({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}=0\]


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