MathematicsOut of a group of swans, 72 times the square roots of the total number are playing on the shore of a pond. The remaining two are swimming in water. Find the total number of swans.

Out of a group of swans, 72 times the square roots of the total number are playing on the shore of a pond. The remaining two are swimming in water. Find the total number of swans.


  1. A
    0
  2. B
    4
  3. C
    16
  4. D
    8 

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    Solution:

    Concept- Using the method of quadratic factorization by splitting the middle term then we will apply the conditions given in the equation.
    Given 72 times of the square root of the total number of swans n, i.e.
    Adding the remaining two swans that are swimming, then we get,
    72n+2=n
    72n=n-2
    On squaring both sides, we get
    72n=4(n-2) 2
    49n=4(n2-4n-4) 
    By using identity (a-b) 2=a2+b2-2ab, we get
    49n=4n2-16n+16
    4n2-65n+16=0
    By using the method of factorization, and splitting the middle term, we will get,
    4n2-n-64n+16=0
    n(4n-1) -16(4n-1) =0
    Taking (4n-1) as common, we get
    (4n-1) (n-16) =0
    Now, either the values of n=14 or n=16
    As, the number of swans cannot be in the form of fraction =14, there the correct answers =16
    The total number of swans = 16
    Hence, the correct answer is option 3.
     
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