Question

    If two numbers add up to 12 and the sum of their cubes

    is 1728, then what is the product of the two numbers?
    A 1 Correct Answer Incorrect Answer
    C 4 Correct Answer Incorrect Answer
    D 8 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the two numbers be 'a' and 'b'. a + b = 12 a³ + b³ = 1728 We know that, (a + b)³ = a³ + b³ + 3ab × (a + b) Or, (12)³ = 1728 + 3ab × 12 Or, 1728 = 1728 + 36ab Or, 1728 = 1728 + 36ab So, 36ab = 0 ⇒ ab = 0 Hence, Product of the numbers = 0

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