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.

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#### Solution

Let the total number of swans be *x*.

Then, total numbers 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`

2y^{2} = 7y + 4

2y^{2} - 7y - 4 = 0

2y^{2} + 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, we get

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

x = 16

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

Is there an error in this question or solution?

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