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    Question

    If a + b + c = 18, and a ³ + b ³ + c ³ - 3abc = 54, hen

    find the value of 5(ab + bc + ca).
    A 320 Correct Answer Incorrect Answer
    B 250 Correct Answer Incorrect Answer
    C 535 Correct Answer Incorrect Answer
    D 328 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Given, a + b + c = 18

    We know that,
    Image
    So, 54 = 18 × (18²−3(ab + bc + ca))

    54 = 18 × (324 − 3(ab + bc + ca))

    Divide both sides by 18:

    3 = 324 −3(ab + bc + ca)

    3(ab + bc + ca) = 321

    ab + bc + ca =107

    So, required value = 5 × 107= 535

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