Question

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

Answer 1

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Answer 2

Answer:

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.

To find

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

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,

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

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

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

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

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

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

Put √x = y

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

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

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

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

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

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

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

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

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

the total number of birds is 576