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    Question

    In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer:

    I. x2 – 3(x + 5) = -11 II.

    y2 – 4(y + 2) = -2y
    A if x > y Correct Answer Incorrect Answer
    B if x ≥ y Correct Answer Incorrect Answer
    C if x < y Correct Answer Incorrect Answer
    D if x ≤ y Correct Answer Incorrect Answer
    E if x = y or the relationship cannot be established Correct Answer Incorrect Answer

    Solution

    I. x2 – 3(x + 5) = -11 => x2 – 3x - 15 = -11 => x2 – 3x - 4 = 0 => x2 – 4x + x – 4 = 0 => x(x – 4) + 1(x – 4) = 0 => (x – 4) (x + 1) = 0 => x = 4, -1 II. y2 – 4(y + 2) = -2y => y2 – 4y – 8 = -2y => y2 – 2y – 8 = 0 => y2 – 4y + 2y - 8 = 0 => y(y – 4) + 2(y – 4) = 0 => (y – 4) (y + 2) = 0 => y = 4, -2 Hence, the relationship between x and y cannot be established.

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