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The sum of a number and its positive square root is $\frac{6}{25}$. Find the number.
Given:
The sum of a number and its positive square root is $\frac{6}{25}$.
To do:
We have to find the number.
Solution:
Let the required number be $x^2$.
This implies,
The positive square root of the number is $x$.
According to the question,
$x^2+x=\frac{6}{25}$
$25(x^2+x)=6$
$25x^2+25x-6=0$
Solving for $x$ by factorization method, we get,
$25x^2+30x-5x-6=0$
$5x(5x-1)+6(5x-1)=0$
$(5x+6)(5x-1)=0$
$5x+6=0$ or $5x-1=0$
$5x=-6$ or $5x=1$
$x=\frac{-6}{5}$ or $x=\frac{1}{5}$
The square root of the required number is positive. Therefore, $x=\frac{1}{5}$
$x^2=(\frac{1}{5})^2=\frac{1}{25}$
The required number is $\frac{1}{25}$.
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