Question

please solve the underlined question

Answer 1

the number is 1/25





hope this helps

Answer 2

Answer:

Step-by-step explanation:

Solution :

Given :

The sum of a number & it's positive square root is $\frac{6}{25}$

Let the number be x,

Then,

$x + \sqrt{x} = \frac{6}{25}$ ---> (1)

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Let  x = y² (to obtain a quadratic equation, we should remove square root)

⇒ $y^2 + \sqrt{y^2} = \frac{6}{25}$

⇒ $y^2 + y = \frac{6}{25}$

⇒ $y^2 + y - \frac{6}{25}=0$

⇒ $25y^2 + 25y - 6 = 0$

⇒ $25y^2 - 5y + 30y - 6 = 0$

⇒ $5y(5y - 1) +6(5y - 1) = 0$

⇒ $(5y + 6)(5y - 1) = 0$

⇒  $5y + 6 = 0 (or) 5y-1 = 0$

⇒ $y = \frac{-6}{5} (or) y = \frac{1}{5}$

⇒ $y = \frac{1}{5}$ (As, $y = \frac{-6}{5}$ doesn't give 6/25)

⇒ $x = (\frac{1}{5})^2$

⇒ $x = \frac{1}{25}$ ,.

⇒ $x + \sqrt{x} = \frac{1}{25} + \sqrt{\frac{1}{25} } = \frac{1}{25} + \frac{1}{5} = \frac{6}{25}$

Hence, $x = \frac{1}{25}$

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