Out of a number of saras birds, one-fourth of the number are moving about in lotus plants, 1/9th coupled along with 1/4th as well as 7 times the square root of the number move on a hill. 56 birds remain in vakula trees. What is the total number of birds?

Explanation

Let, the total number of Saras birds be x.
`because` Number of brids moving about in lotus plants `=(x)/(4)`
Number of birds moving on a hill `(x)/(9)+(x)/(4)+7sqrtx`
Number of birds remaining in Vakula trees = 56
`because(x)/(4)+(x)/(9)+(x)/(4)+7sqrtx+56=x`
`impliesx-(x)/(4)-(x)/(9)-(x)/(4)=7sqrtx+56`
`implies(36x-9x-4x-9x)/(36)=7sqrtx+56`
`implies(14x)/(36)=7sqrtx+56`
`implies(x)/(18)=sqrtx+8`
`impliesx-18sqrtx-144=0" "........(1)`
Let `sqrtx=y,` then (1) becomes
`y^(2)-18y-144=0`
`(y-24)(y+6)=0`
`becausey=24ory=-6`
`impliessqrtx=24orsqrtx=-6`
but square root of a positive number cannot be negative.
So, we reject `sqrtx=-6`
`becausesqrtx=-(10)/(3)impliesx=576" "("on squaring")`
Hence, the total number of Saras birds = 576.