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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. - CBSE Class 10 - Mathematics

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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.

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`

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, we get

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

x = 16

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

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Solution 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. Concept: Solutions of Quadratic Equations by Factorization.
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