Question

The sum of a number and its positive square root is 6/25. Find the number.​

Answer 1

Answer:

Given:

Sum of a number and its positive square root is 6/25.

To find:

Value of that unknown number.

Solution:

Let the number be x. Then, its positive square root will be $\sqrt{x}$

ATQ,

$x + \sqrt{x} = \frac{6}{5} \\ \\ \Longrightarrow \: 25x + 25 \sqrt{x} = 6 \\ \\ \Longrightarrow25x + 25 \sqrt{x} - 6 = 0 \: \: \: \: \: \: equation \: (1)$

$let \: \: \sqrt{x} = y \\ \\ or \: \: x = {y}^{2}$

Then,

equation 1 becomes

$25 {y}^{2} + 25y - 6 = 0 \\ \\\Longrightarrow25 {y}^{2} + 30y - 5y - 6 = 0 \\ \\\Longrightarrow5y(5y + 6) - 1(5y + 6) = 0 \\ \\ \Longrightarrow(5y + 6)(5y - 1) = 0$

Therefore, y = -6/5 or 1/5.

Now, substituting the value of y in equation 2, we get,

$\sqrt{x}$ = 1/5

x = 1/25

$\sqrt{x}$= 6/5 which is not possible because $\sqrt{x}$ is positive.

Hence, the required number is 1/25.