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    Question

    In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

    I. x2 – 7x + 12 = 0 II.

    y2 – 7y + 10 = 0
    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 relation cannot be established Correct Answer Incorrect Answer

    Solution

    I. x2 – 7x + 12 = 0 => x2 – 4x – 3x + 12 = 0 => x(x – 4) – 3(x – 4) = 0 => (x – 4) (x – 3) = 0 => x = 4, 3 II. y2 – 7y + 10 = 0 => y2 – 5y – 2y + 10 = 0 => y(y – 5) – 2(y – 5) = 0 => (y – 5) (y – 2) = 0 => y = 5, 2 Hence, relation cannot be established. Alternate Method: if signs of quadratic equation is -ve and +ve respectively then the roots of equation will be +ve and +ve. So, roots of first equation = x = 4, 3 So, roots of second equation = y = 5, 2 After comparing we can conclude that relationship cannot be established between x and y.

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