Question

Out of a group of swans, 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

Let the total number of swans be x.

Then, the total number of swans are playing on the share of a pond `7/2 sqrtx.`

It is given that

`7/2 sqrtx + 2 = x`

Let x = y², then `7/2 y+2=y^2`

`(7y+4)/2=y^2`

2y² = 7y + 4

2y² - 7y - 4 = 0

2y² - 8y + y - 4 = 0

2y(y + 4) - 1(y + 4) = 0

(2y - 1)(y + 4) = 0

2y - 1 = 0

2y = 1

y = 1/2

Or

y + 4 = 0

y = -4

Because y = 1/2 is not correct.

Thus, y = -4 is correct. Putting the value of y

y = -4

`sqrtx= -4`

Square root both sides and we get

`(sqrtx)^2=(-4)^2`

x = 16

Therefore, the total number of swans is x = 16.