Question:
The sum of a number and its positive square root is 6/25. Find the number.
Solution:
Let first numbers be x
Then according to question
$x+\sqrt{x}=\frac{6}{25}$
Let $x=y^{2}$ then
$y^{2}+y=\frac{6}{25}$
$25 y^{2}+25 y=6$
$25 y^{2}+25 y-6=0$
$25 y^{2}+30 y-5 y-6=0$
$5 y(5 y+6)-1(5 y+6)=0$
$(5 y+6)(5 y-1)=0$
$(5 y+6)=0$
$y=\frac{-6}{5}$
Or
$(5 y-1)=0$
$x=\frac{1}{5}$
Since, being a positive number, so y cannot be negative.
Therefore,
$x=y^{2}$
$=\left(\frac{1}{5}\right)^{2}$
$=\left(\frac{1}{25}\right)$
Thus, the required number be $\left(\frac{1}{25}\right)$