Let the number of swans in the pond be ‘a’.
Given, 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.
\(\Rightarrow \frac{7}{2}\sqrt{a}+2=a\)
⇒ 7√a = 2a – 4
Squaring both sides
⇒ 49a = 4a2 + 16 – 16a
⇒ 4a2 – 65a + 16 = 0
⇒ 4a2 – 64a – a + 16 = 0
⇒ 4a(a – 16) – (a – 16) = 0
⇒ (4a – 1)(a – 16) = 0
⇒ a can’t be 1/4,
thus a = 16