Question

Out of a group of swans, $\frac{7}{2}$ times the square root of the number are playing on the shore of a tank. The two remaining ones are playing, with amorous fight, in the water. What is the total number of swans?

Answer 1

Let the total number of swans be $x$.

Then,Number of swans playing on the shore of the tank $=\frac{7}{2}\sqrt{x}$
It is given that there are two remaining swans
$\therefore x=\frac{7}{2}\sqrt{x}+2$

$\Rightarrow x-\frac{7}{2}\sqrt{x}-2=0$

$\Rightarrow y^2-\frac{7}{2}y-2=0$ (where $y^2=x$)

$\Rightarrow 2y^2-7y-4=0$

$\Rightarrow 2y(y-4)+(y-4)$

$\Rightarrow y=4ory=-\frac{1}{2}$

$\Rightarrow$ $y=4$ ($\because y=-\frac{1}{2}$ is not possible)

$\Rightarrow x=y^2=4^2=16$

Hence the total number of swans is $16$.