Question

Out of a number of birds ,one-fourth of the number are moving about lotus plants 1 upon 9th along with 1 upon 4th as well as 7 times the square root of the number movesbon a hill 56 birds remain in vakula trees .what is the total number of birds

please give the proper explanation of this sum and this sum is of 10th std textbook .
please give properly .
write in sequence and send me the answer
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Answer 1

Given :

Out of a number of birds,

1/4 of the number are moving about lotus plant

1/9 along with 1/4 as well as 7 times the square root of the number move on a hill

56 birds remain in vakula trees.

To Find :

Total number of birds

Solution :

Let the number of birds = $\sf x^2$

Number of birds moving about lotus plant =$\frac{ {x}^{2} }{4}$

Number of birds along with = $\frac{ {x}^{2} }{9}$

Number of birds moves on hill =$7x$

Number of birds remaining on tree = $56.$

According to question :

$\frac{ {x}^{2} }{4} +\frac{ {x}^{2} }{4} + \frac{ {x}^{2} }{9} + 7x \: + 56 = {x}^{2}$

$\frac{ {11x}^{2} }{18} + 7x + 56 = {x}^{2}$

$\frac{ {11x}^{2} }{18} - {x}^{2} + 7x + 56 = 0$

$- \frac{ {7x}^{2} }{18} + 7x + 56 = 0$

${x}^{2} - 18x - 114 = 0$

${x}^{2} - 24x + 6x + 114 = 0$

$x( x-24) +6(x-24) \: = 0$

$(x-24)(x+6) =0$

$x = 24 \: and \: x = - 6$

x can't be negative so -6 will be discarded

So x = 24

and x² = 576

Thus total number of birds are 576.

Answer 2

AnswEr :

Let us Consider that number of Birds are = $\sf x^2$

The number of Birds moving about lotus plants = $\sf\dfrac{x^2}{4}$

Number of Birds along = $\sf\dfrac{x^2}{9} + \dfrac{x^2}{4}$

And, the Number of Birds who are moving on a Hill = $\sf \: 7 \sqrt{x^2}$

$:\implies\sf 7x$

Remain Birds = 56

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As Per Given Question -

$:\implies\sf \dfrac{x^2}{4} + \dfrac{x^2}{4} + \dfrac{x^2}{9} + 7x + 56 = x^2$

$:\implies\sf \dfrac{11 \: x^2}{18} + 7x + 56 = x^2$

$:\implies\sf 7x + 56 = \dfrac{7 x^2}{18}$

$:\implies\sf 7x^2 - 136x - 1008 = 0$

$:\implies\sf x^2 - 18x - 144 = 0$

$:\implies\sf x^2 - 24x + 6x - 144 = 0$

$:\implies\sf x(x - 24) + 6(x - 24) = 0$

Now, Comparing these factors with 0.

$:\implies\sf x - 24 = 0$

$:\implies\sf\red{x = 24}$

$:\implies\sf x + 6 = 0$

$:\implies\sf\red{x = -6}$

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$:\implies\sf x^2 \:\:\:\:\:\:\:\:\:\:\:\:\:\:\ [ x = 24]$

$:\implies\sf 24 \times 24$

$:\implies\sf\pink{576}$

Hence, Total Number of Birds are = 576.