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    Question

    I. x=  √(20+ √(20+ √(20+

    √(20…………….∞)) ) )Β  II. y= √(5√(5√(5√(5……….∞)) ) )Β  In each of these questions, two equations numbered I and II are given. You have to solve both the equation and mark the appropriate option – give answer
    A If, x>y Correct Answer Incorrect Answer
    B If, xβ‰₯y Correct Answer Incorrect Answer
    C If, x Correct Answer Incorrect Answer
    D If, x≀y Correct Answer Incorrect Answer
    E If, x=y or relationship between x and y cannot be established. Correct Answer Incorrect Answer

    Solution

    I. x=  √(20+ √(20+ √(20+ √(20…………….∞)) ) )Β  x= √(20+x)Β  By squaring both sides, x^2=20+xΒ  x^2- x-20=0Β  x^2- 5x+4x-20=0Β  x(x-5)+4(x-5)= 0Β  x= Β 5,-4Β  II. y= √(5√(5√(5√(5……….∞)) ) )Β  y= √5yΒ  By squaring both sides, y^2=5yΒ  y=5Β  Hence, x≀y

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