Question

Out of a number of Saras birds, one fourth the number are moving about lotus plants, 1/9th (one nineth) coupled (along) with 1/4th (one fourth) as well as7 times the square root of number move on a hill, 56 birds remain in vakula trees. What is the total number of birds?

Please solve and tell me.

Answer 1

by solving last equation you can get your answer

if helped plz make it brainiest and if wrong than sorry

Answer 2

Let the total number of birds = x

Birds moving in lotus plants = $\sf{\frac{1}{4}x}$

Birds moving on a hill = $\sf{\frac{1}{9} x + \frac{1}{4} x + 7 \sqrt{x} }$

According to the question, the total number of birds will be

= $\sf{\frac{1}{4} x + \frac{1}{9} x + \frac{1}{4} x + 7 \sqrt{x} + 56 = x}$

Multiplying each term by 36, we get

= $\sf{9x + 4x + 9x - 36x + 7 \times 36 \sqrt{x} + 56 \times 36 = 0}$

= $\sf{- 14x + 7 \times 36 \sqrt{x} + 56 \times 36 = 0}$

Dividing both sides by (-14), we get

= $\sf{x-18√x-144=0}$

Is is Quadratic in √x

= $\sf{ {( \sqrt{x} )}^{2} - 24 \sqrt{x} + 6 \sqrt{x} - 144 = 0}$

= $\sf{ \sqrt{x} ( \sqrt{x} - 24) + 6( \sqrt{x} - 24) = 0}$

= $\sf{( \sqrt{x} + 6)( \sqrt{x - 24)} = 0}$

= $\sf{\sqrt{x} = 24 \: or \: \sqrt{x} = - 6}$

= $\sf{x = {(24)}^{2} = 576}$

Hence, the total number of birds = 576