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.

Question

Philoid · Accepted Answer

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.

⇒ 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