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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

ConceptSolutions of Quadratic Equations by Factorization

#### 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.

Is there an error in this question or solution?

#### APPEARS IN

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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