Question

Out of a group of Swans 7/2 times the square root of the total number are playing on the shore of a river bank. The two remaining ones are playing in the water. Find the total number of Swansea.

Answer 1

Hope u like my process
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=> Let the total number of swans be x

=> so, swans playing in water = 2

=> swans playing on the shore = x-2

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By problem
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$= > \bf \: x - 2 = \frac{7}{2} \sqrt{x} \\ \\ = > 2x - 4 = 7 \sqrt{x} \\ \\ \bf \underline{squaring \: \: both \: \: sides} \\ \\ = > {(2x - 4)}^{2} = {(7 \sqrt{x} )}^{2} \\ \\ = > 4 {x}^{2} - 16x + 16 = 49x \\ \\ = > 4 {x}^{2} - 16x + 16 - 49x = 0 \\ \\ = > 4 {x}^{2} - 65 +16= 0$
$= > 4 {x}^{2} - 64x - x + 16 = 0 \\ \\ = > 4x(x - 16) - 1(x - 16) = 0 \\ \\ = > (x - 16)(4x - 1) = 0 \\ \\ \bf \underline{since \: \: the \: \: number \: \: of \: \: swans \: \: can't \: \: be \: \: fraction} \\ \\ = > x - 16 = 0 \\ \\ = > \bf \: x = 16$
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So the total number of swans is 16
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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.