Question

Out of a number of saras birds, one-fourth of the number are moving about in lots, $\frac{1}{9}\mathrm{th}$ coupled with $\frac{1}{4}\mathrm{th}$ 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?

Answer 1

$$\begin{gathered} \text{Let the total number of birds be}{x}^2. \\ \text{According to the question:} \\ \frac{x^2}{4}+(\frac{x^2}{9}+\frac{x^2}{4})+7x+56=x^2 \\ \Rightarrow \frac{9x^2+4x^2+9x^2+252x+2016}{36}=x^2 \\ \Rightarrow 22x^2+252x+2016=36x^2 \\ \Rightarrow 14x^2-252x-2016=0 \\ \Rightarrow x^2-18x-144=0 \\ \Rightarrow x^2-24x+6x-144=0 \\ \Rightarrow x(x-24)+6(x-24)=0 \\ \Rightarrow (x-24)(x+6)=0 \\ \Rightarrow x=24\text{or}x=-6 \\ \therefore x=24(\because \mathrm{N}\text{umber of birds cannot be negative}) \\ \therefore \mathrm{N}\text{umber of birds}=x^2=576 \end{gathered}$$