Question

Out of a group of swans, 7/2 times the square root of the no. are playing on the shore of a bank. the remaining ones are playing with amourous flight, in the water. what is the total no, of swans? (bhaskara born 1114 AD)

Answer 1

Out of a group of swans, times the square root of the number are playing on the shore of a bank. The remaining two are playing with amorous flight, in the water. what is the total no. of swans? Then here is the solution: Let the number of swans be x2. Then number of swans playing at the bank shore Number of swans playing in water = 2 Total number of swans = No. of swans playing at bank shore + No. of swans playing in water ⇒ 2x2 = 7x + 4 ⇒ 2x2 – 7x – 4 = 0 ⇒ 2x2 – 8x + x – 4 = 0 ⇒ 2x (x – 4) + (x – 4) = 0 ⇒ (2x + 1) ( x – 4) = 0 ⇒ 2x + 1 = 0 or x – 4 = 0 But n = is not feasible. Thus, x = 4 Hence, number of swans = x2 = 42 = 16.

Answer 2

Let the totɑl number of swɑns be x.
Number of swɑns plɑying on the shore of ɑ tɑnk = 7√x/ 2.
Given: Remɑining swɑns = 2
x=7√x /2 +2
x-2 = 7√x /2
2(x-2) = 7√x
2(x-2)² = (7√x)²

[On squɑring ring both sides]
4(x-2)² = 49x
4(x²-4x+4) = 49x

[ (ɑ-b)² = ɑ² -2ɑb +b²]

4x²-64x+16 -49x= 0
4x²- 16x+16 -49x= 0
4x² - 65x +16= 0
4x² -64x  - x +16= 0
4x (x -16) -1(x-16)=0
(x-16) (4x -1) = 0
x-16 = 0 or 4x-1 = 0

x = 16 or x = 1/4
Since, the number of swɑns cɑnnot be ɑ Frɑction ( ¼).

So,  x = 16
Hence,The totɑl number of swɑns = 16.