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    Question

    Directions (Q.21-25): In the following questions, two equations numbered I and II are given. You have to solve both the equations and find out the correct option. Give answer

    I. 2 x ² - (4 + √13) x + 2√13 = 0

    II. 10 y ² - (18 + 5√13) y + 9√13 = 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 Correct Answer Incorrect Answer
    E If x=y or relationship between between x and y cannot be established Correct Answer Incorrect Answer

    Solution

    I. 2 x ² - (4 + √13) x [if gte msEquation 12]>x [if !msEquation]--> [endif]-->+ 2√13 = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]-->2 x ² - 4 x - √13x + 2√13 = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]-->2 x ( [if gte msEquation 12]>x [if !msEquation]--> [endif]-->x – 2) - √13 ( [if gte msEquation 12]>x [if !msEquation]--> [endif]-->x– 2) = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]-->( [if gte msEquation 12]>x [if !msEquation]--> x-2) (2 x - √13) = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]--> x = 2, `(sqrt(13))/(2)` [if gte msEquation 12]> √13 2 [if !msEquation]--> [endif]--> II. 10 y ² - (18 + 5√13) y [if gte msEquation 12]>y [if !msEquation]--> [endif]-->+ 9√13 = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]-->10 y ² - 18 y - 5√13 y + 9√13 = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]-->2 y (5 y – 9) - √13 (5 y – 9) = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]-->(2 y – √13) (5 y – 9) = 0 [if gte msEquation 12]>⇒ [if !msEquation]--> [endif]--> y = `(sqrt(13))/(2)` [if gte msEquation 12]> √13 2 [if !msEquation]--> [endif]-->,`(9)/(5)` [if gte msEquation 12]> 9 5 [if !msEquation]--> [endif]--> Hence, x [if gte msEquation 12]>x [if !msEquation]--> [endif]-->≥ y [if gte msEquation 12]>y [if !msEquation]--> [endif]-->

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