Question

one fourth of the herd of goats was seen in the forest twice the square root of the number of herd had gone up the hill and their the remaining 15 goats were on the bank of the river find the total number of goats​

Answer 1

Answer:

total number of goat = 36

Step-by-step explanation:

let total number of goat be x

goats in forest 1/4x

goats up on hill 2√x

remaining goats 15

$\frac{1}{4} x + 2 \sqrt{x} + 15 = x \\ \frac{x + 8 \sqrt{x} + 60}{4} = x \\ x + 8 \sqrt{x} + 60 = 4x \\ 3x - 8 \sqrt{x} - 60 = 0 \\ 3 { (\sqrt{x}) }^{2} - 8 \sqrt{x} - 60 = 0 \: \: \: \: \: \: \: \:( x = \sqrt{x} \times \sqrt{x}) \\ 3 {( \sqrt{x} )}^{2} - 18 \sqrt{x} + 10 \sqrt{x} - 60 = 0 \\ 3 \sqrt{x} ( \sqrt{x} - 6) + 10( \sqrt{ x } - 6) = 0 \\ (3 \sqrt{x} + 10)( \sqrt{x} - 6) = 0 \\ 3 \sqrt{x} + 10 = 0 \: \: \: \: \sqrt{x} - 6 = 0 \\ 3 \sqrt{x} = - 10 \: \: \: \: \: \: \sqrt{x} = 6 \\ \sqrt{x} = - \frac{10}{3} \: \: \: \: \: \: {( \sqrt{x} )}^{2} = {6}^{2} \\ we \: take \: the \: positive \: value \\ x = 36$

number of goat in forest = 1/4 × x = 1/4 × 36 = 9

number of goat on hill = 2√x = 2×√36= 2×6=12

remaining goats = 15

9+12+15 = 36

hope you get your answer

Answer 2

Answer:

36 .

Step-by-step explanation:

Let the total number of camel be x .

No. of camel seen in forest = x / 4

No. of camel gone to mountains = 2 √ x

No. of camel seen on bank of river = 15

Total no. of camel .

x / 4 + 2 √ x + 15

x = x / 4 + 2 √ x + 15

3 x - 60 = 8 √ x

Squaring on both sides:

64 x = 9 x² - 360 x + 3600

9 x² - 424 x + 3600 = 0

( x - 36 ) ( 9 x - 100 ) = 0

x = 36 or x = 100 / 9

Since camels cannot be in fraction .

Hence final answer i.e. total numbers of camels are 36.