Out of a number of saras birds, one-fourth of the number are moving about in lots, coupled with coupled with th as well as 7 times the square root of the number move on a hill, 56 birds remain in vakula trees. The total number of birds is ____.

Question

Out of a number of saras birds, one-fourth of the number are moving about in lots, coupled with coupled with th as well as 7 times the square root of the number move on a hill, 56 birds remain in vakula trees. The total number of birds is ____.

Accepted Answer

Concept- The total number of birds would be 576. In order to answer this question, we must first assume that there are an infinite number of birds. Then, we must add all of the numbers of Sara's birds that participate in various activities together, since this will equal the total number of birds. Finally, we must solve the resulting equation to determine the total number of birds.
A total number of Saras birds should exist

Number of birds moving about in lots is

Now it is also been given that

of the Saras bird is coupled with

of birds then,
total birds coupled

Also it is given that 7 times the square root of the number of birds move on a hill

iii )
There are still several birds in the vakula trees

Now since we have a total number of

Saras birds, hence we can write the equation by adding (i) , (ii) , (iii) &
(iv) as

Now let us assume

, hence we can rewrite the equation as

By further solving this equation we can write

Since the aforementioned equation is now in quadratic form, we may factorize the middle term to determine the two roots of the equation.

So we can write

Now that we have calculated the number of birds, we will omit because it can never be negative

,
so we can write

Since we have taken

, where

,
Hence, we can write

= x^{2} = 2 4^{2} = 576

So, the total numbers of birds

Hence, the correct answer is 576

Out of a number of saras birds, one-fourth of the number are moving about in lots, coupled with coupled with th as well as 7 times the square root of the number move on a hill, 56 birds remain in vakula trees. The total number of birds is ____.

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