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    Question

    If a, b and c are integers such that a 2  +

    b 2  + c 2  = 228, a + b + c = 26 and b = c, then find the value of a?
    A 6 Correct Answer Incorrect Answer
    B 8 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 10 Correct Answer Incorrect Answer

    Solution

    We know, (a + b + c) 2  = a 2  + b 2  + c 2  + 2(ab + bc + ac)

    Then, 26 2  = 228 + 2(ab + b 2  + ab)

    224 = b(2a + b)

    And, a + b + b = 26

    a = 26 - 2b

    Now, 224 = b(2(26 - 2b) + b)

    b = 8, 28/3 (but b is an integer)

    Then, b = 8 = c

    Therefore, a = 26 - 2 * 8 = 10

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