Question

The sum of a number and its positive square root is $\frac{6}{25}$. Find the number. If the number is $\frac{1}{m}$ then find the value of $m$.

Answer 1

Let no. be $n^2$.

$\therefore n^2+\sqrt{n^2}=\frac{6}{25}$

$⟹25n^2+25n-6=0$

$⟹25n^2+30n-5n-6=0$

$⟹5n(5n+6)-1(5n+6)=0$

$⟹(5n-1)(5n+6)=0$

$⟹n=\frac{1}{5}$ {Because Square root is positive}

$⟹n^2=\frac{1}{25}=\frac{1}{m}$

$\therefore m=25$