Answer :

Let the total number of birds be x.

Condition: One fourth the number are moving about in lotus plants;

^{ th }coupled(along) with

^{ th }as well as 7 times the square root of the number

move on a hill; 56 birds remain in vakula trees.

324x = x ^{ 2 } – 288x + 20736

x ^{ 2 } – 612x + 20736 = 0

x ^{ 2 } - 576x – 36x + 20736 = 0

x(x – 576) – 36(x – 576) = 0

(x – 36)(x – 576) = 0

(x – 36) = 0 or (x – 576) = 0

x = 36 or x = 576

Since the remaining birds where 56 so we neglect the value x = 36.

Therefore the total number of birds are 576.

Checking:

= 64 + 144 + 7× 24 + 144 + 56

= 64 + 144 + 168 + 144 + 56

= 576.

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