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If x is equal to  , where the given expressions extend to an infinite number of roots, then what is the value of x?
  • a)
    -3
  • b)
    -4
  • c)
    3
  • d)
    4
  • e)
    12
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If x is equal to , where the given expressions extend to an infinite n...
Given
  •   to an infinite terms
    • As the value of x is equal to the square root of something, x ≥ 0
To Find:
The value of x
Approach
x=  to an infinite terms.
  • Since the expression under the root extends infinitely, the expression under the root will be equal to x itself.
  • So,  0………….(1)
  • By solving this equation and applying the constraint that x ≥0, we will find the value of x
Working Out
a.
b. Squaring both sides, we have 
As we know that x≥ 0, x = 4
   Answer: D
 
Alternate solution
  • Once we have deduced that x will be positive the options -3 and -4 are eliminated
  • We know √9 is 3. So the value of √(12+ ……) will  be more than 3. Now we are left with 4 and 12 in the options
  • Now √(12 + …..) cannot give us 12..
  • So the answer has be 4.
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