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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.
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Solution
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.
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