Question

Out of a number of birds, one-fourth of the number are moving about the lotus plants,
th along with 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

Step-by-step explanation:

let the birds be x

therefore

4÷x + 7√x + 56 = x

solve further for answer

Answer 2

$\underline\mathfrak{Given:-}$

• Out of a number of birds, one-fourth of the number are moving about the lotus plants.
• the along with th as well as 7 times the square root of the number move on a hill 56 birds remain in vakula trees.

$\underline\mathfrak{To \: \: Find:-}$

• Find the total number of birds ......?

$\underline\mathfrak{Solutions:-}$

• Let the total number of birds = x

• Number of birds moving about in lotus plant = x/4

Number of birds moving on a hill

$\: \: \: \: \: \leadsto \: \: \frac{x}{9} \: + \: \frac{x}{4} \: + \: {7}\sqrt{x}$

Number of birds in vakula tree 56

So,

$\: \: \: \: \: \leadsto \: \: \frac{x}{4} \: + \: {(\frac{x}{9} \: + \: \frac{x}{4} \: + \: {7}\sqrt{x})} \: + \: {56} \: \: = \: \: {x}$

$\: \: \: \: \: \leadsto \: \: {x} \: - \: \frac{x}{9} \: - \: \frac{x}{2} \: - \: {7}\sqrt{x} \: - \: {56} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: \frac{7x}{18} \: - \: {7}\sqrt{x} \: - \: {56} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {7} \: {(\frac{x}{18} \: - \: \sqrt{x} \: - \: {8})} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: \frac{{x} \: - \: {18}\sqrt{x} \: - \: {144}}{18} \:\: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {x} \: - \: {18}\sqrt{x} \: - \: {144} \: \: = \: \: {0}$

Put √x = y

$\: \: \: \: \: \leadsto \: \: {y}^{2} \: - \: {18y} \: - \: {144} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {y}^{2} \: - \: {24y} \: + \: {6y} \: - \: {144} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {y} \: {({y} \: - \: {24})} \: + \: {6} \: {({y} \: - \: {24})} \: \: = \: \: {0}$

$\: \: \: \: \: \leadsto \: \: {({y} \: - \: {24})} \: \: \: {({y} \: + \: {6})}$

$\: \: \: \: \: \leadsto \: \: {y} \: \: = \: {24}, \: {-6} \: \: \: \: but \: \: y \: \: \neq \: \: {-6}$

$\: \: \: \: \: \leadsto \: \: {\sqrt{x}} \: \: = \: {y}$

$\: \: \: \: \: \leadsto \: \: {\sqrt{x}} \: \: = \: {24}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: {(24)}^{2}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: {576}$

So, the total number of birds is 576