Question

out of a group of swans 7/2 times the square root of the total number at playing on the Shore of a pond the two remaining ones are swimming in water find total no. of swans​

Answer 1

Step-by-step explanation:

Let the total number of swans be x.

Therefore, according to the given condition:

$x = \frac{7}{2} \sqrt{x} + 2 \\ multiplying \: throughout \: by \: 2 \\ we \: find : \\ \\ 2 \times x = 2( \frac{7}{2} \sqrt{x} + 2) \\ \\ \therefore 2x = 7 \sqrt{x} + 4 \\ \\ \therefore 2x - 4 = 7 \sqrt{x} \\ squaring \: both \: sides \\ (2x - 4 )^{2} = (7 \sqrt{x} )^{2} \\ \therefore \: 4{x}^{2} - 16x + 16 = 49x \\ \therefore \: 4{x}^{2} - 16x + 16 - 49x = 0 \\ \therefore \: 4{x}^{2} - 65x + 16 = 0 \\ \therefore \: 4{x}^{2} - 64x - x+ 16 = 0 \\ \therefore \: 4{x}(x - 16) -1( x - 16) = 0 \\ \therefore \: (4x - 1)(x - 16) = 0 \\ \therefore \: (4x - 1) = 0 \: or \: (x - 16) = 0 \\ \therefore \: x = \frac{1}{4} \: \: or \: \: x = 16 \\ \\ but \: x \neq \: \frac{1}{4} \\ ( \because \: number \: of \: swans \: can \: not \: be \: \\ a \: fractional \: number) \\ \therefore \: \huge \fbox{x = 16}$

Thus, total number of swans = 16

Answer 2

Answer:

Let the total no. of swans = x

No. of swans playing on the shore = 7/2 √x

Remaining swans = 2

A/Q x=7/2 √x+2

x-2 = 7/2 √x

2(x-2) = 7√x

4(x-2)² = 49x

4(x²-4x+4) = 49x

4x²-65+16 = 0

(x-16) (4x -1) = 0

x-16 = 0 or 4x-1 = 0

x = 16 or x = 1/4

Since, the no. of swans cannot be 1/4

∴ x = 16

The total no.of swans = 16