Question

solve the given question

Answer 1

Solution:

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Given:

Condition 1 :

=>   One - fourth of a herd of camels was seen in the forest.

Let the total number of camels be x.

Then, it means that,

=> $\frac{1}{4} x$,

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Condition 2 :

Twice the square root of the herd had gone to mountains and remaining 15 camels were seen on the bank of the river.

=>$2 \sqrt{x} + 15$

Hence the equation is :

$\frac{1}{4} x + 2 \sqrt{x} + 15 = x$ ....(i)   (Total number of camels)

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To find :

The total number of camels.(Value of x)..

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As, we found an equation for total number of camels in (i),

If we substitute x = y² (to get a quadratic equation),

=> $\frac{1}{4} y^{2} + 2 \sqrt{y^2} + 15 = (y)^{2}$

=> $- \frac{3}{4} y^2 +2y+15 = 0$

Multiplying the equation by 4 (To cancel the fraction)

We get,

=> $-3y^2 + 8y + 60 = 0$

Multiplying the equation by ( -1) (To remove negative sign in - 3y²)

We get,

=> $3y^2 - 8y - 60 = 0$ ...(ii)

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=> 3y² - 18 y + 10 y - 60 = 0,

=> 3y(y - 6) + 10 (y - 6) = 0,

=>(3y+ 10)(y - 6) = 0,

0 x anything is 0,

So,

For the equation to be 0,

Either 3y + 10 = 0 (or) y - 6 = 0,

=> 3y = - 10  (or) y = 6,

=> $y = \frac{-10}{3}$ (or) y = 6,

=> y ≠  $\frac{-10}{3}$ (as y cannot be negative & can't be in fraction)

∴ y = 6,.

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We know that, y² = x

∴ Total number of camels

=> (6)² = 36,.

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