Question

Out of a group of swans, 7 /2 times the square root of the number are playing on the sea shore of a tank. The two remaining ones are playing in the water. What is the total number of swans?

Answer 1

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 ring 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
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 ( ¼).

So,  x = 16
Hence,The total number of swans = 16.

HOPE THIS WILL HELP YOU..

Answer 2

Heya,

Let the total no. of swans = x

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

Remaining swans = 2

According to the question:-

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

Therefore, 【x = 16】 ANSWER...

HOPE IT HELPS:-))