Question

Out of a group of swans, $\frac{7}{2}$ times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.

Answer 1

SOLUTION :  

Let the total number of swans be x.

Number of swans playing on the shore of a tank = 7√x/ 2.

Given: Remaining swans = 2

x=7√x /2 +2

x-2 = 7√x /2  

2(x-2) = 7√x

2(x - 2)² = (7√x)²

[On squaring both sides]

4(x - 2)² = 49x

4(x² - 4x+ 4) = 49x

[ (a-b)² = a² -2ab +b²]

4x² - 64x + 16 - 49x = 0

4x² - 16x + 16 - 49x =  0

4x² - 65x + 16 = 0

4x² - 64x  - x + 16 = 0

[By middle term splitting]

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 swans cannot be a Fraction .so x ≠ 1/4

Therefore , x = 16

Hence,the total number of swans = 16.

HOPE THIS  ANSWER WILL HELP YOU..

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.