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.

Answer 1

$\textbf{Answer}$

Suppose the total number of swans is x.

Since $\textbf{7/2 times the square root of total}$ number of swans are playing in the pond.
&
$\textbf{Two swans are swinging}$ in water.

=> x = 7/2 (√x) + 2

=> x - 2 = 7/2 (√x)

=> 2x - 4 = 7(√x)

$\textbf{Squaring both sides now,}$

=> (2x - 4)^2 = 49x

=> 4x^2 + 16 - 16 x = 49x

=> 4x^2 - 65 x + 16 = 0

=> 4x^2 - 64x - x + 16 = 0

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

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

=> x = 16 or x = 1/4

But x is the number of total swans, which must be a positive whole number.

=> x = 16

$\textbf{So the total number of swans is 16}$

$\textbf{Hope It Helps}$

$\textbf{Thanks}$

Answer 2

your answer is 16
x=16