Question

one of group of 7 /2 time the square root of the total number are playing on the Shore of tank the two remaining ones are playing with amorous fight in the water what is the total number of Sawan​

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