math solution?

Question

Out of a number of Saras birds, 1/4 th the number are moving about in lotus plants , 1/9 th coupled(along) with 1/4 th as 7 times the square root of the number move on a hill , 36 birds remain in bakula trees . What is the total no. of birds.
Ans=576( The question is taken from a practise guide for exam namedHFI EDUCATION TODAY FOR IX-X PUBLISHED IN FEB-2004 >

Answer 1

Let say total no of birds = x
1/4 x moving about in lotus plants.
1/9 x coupled with 1/4 x.
7 sqrt (x) move on hill.
56 birds remains in bakula trees.
(should be 56 not 36 birds remain)

So,
1/4 x + 1/9 x + 1/4 x + 7sqrt (x) + 56 = x
7 sqrt(x) = x - 1/4x - 1/9x - 1/4 x - 56
7 sqrt(x) = 14/36 x - 56 ---(1)
36 sqrt(x) = 2x - 288
18 sqrt(x) = x - 144
Suare both sides
324 (x) = (x - 144)^2
324x = x^2 - 288x + 20736
x^2 - 612x + 20736 = 0
(x - 576)(x - 36) = 0
x = 576 or 36
From (1)
7 sqrt(x) = 14/36 x - 56 must be positive at both sides
So, x <> 36 (x must be larger than 56 birds remain)
x = 576