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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    Find the value of \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]when \[a=225,\]\[b=226,\]\[c=227.\]

    A) 2304

    B) 2430

    C) 2034

    D) 2340

    Correct Answer: C

    Solution :

    [c] We know that,\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\] \[=\frac{(a+b+c)\frac{1}{2}[{{(a-b)}^{2}}]+{{(b-c)}^{2}}+{{(c-a)}^{2}}]}{2}\] \[=(225+226+227).\frac{1}{2}[1+1+4]\] \[=678\times 3=2034\]


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