Question

out of a group of swans, 3.5 times the square root of the number are playing on the shore of a tank. The remaining two are playing in the water. find the total number of swans.

Answer 1

i am sending you answer of an example question seeing this solve on your own

Let the total no. of swans = x

No. of swans playing on the shore = 7/2 √x

Remaining swans = 2

A/Q x=7/2 √x+2

x-2 = 7/2 √x

2(x-2) = 7√x

4(x-2)² = 49x

4(x²-4x+4) = 49x

4x²-65+16 = 0

(x-16) (4x -1) = 0

x-16 = 0 or 4x-1 = 0

x = 16 or x = 1/4

Since, the no. of swans cannot be 1/4

∴ x = 16

The total no.of swans = 16

Answer 2

Just as Sona mam has told you an example, in just the same way I have done it also.:------

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.