# Out of a number

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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