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      Question

      I. x=  √(20+ √(20+ √(20+

      √(20…………….∞)) ) )  II. y= √(5√(5√(5√(5……….∞)) ) )  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, x≥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…………….∞)) ) )  x= √(20+x)  By squaring both sides, x^2=20+x  x^2- x-20=0  x^2- 5x+4x-20=0  x(x-5)+4(x-5)= 0  x=  5,-4  II. y= √(5√(5√(5√(5……….∞)) ) )  y= √5y  By squaring both sides, y^2=5y  y=5  Hence, x≤y

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