Question

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

Answer 1

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Answer 2

The value of number is $\frac{1}{25}.$

Solution:

Let us take the number as X, now the question says that the sum of square root and the number forms the solution $\frac{1}{25}.$

Hence, the sum is $X+\sqrt{X}=\frac{6}{25}$

Now let us take $\sqrt{X}=t$we get the equation of $X+\sqrt{X}=\frac{6}{25} \text { as } t^{2}+t-\frac{6}{25}=0$

Simplifying the equation we get $25 t^{2}+25 t-6$. Let us find the roots of the equation we get

$5 t(5 t+6)-1(5 t+6)=0$

(5t+6)(5t-1)=0  

$t=-\frac{6}{5} ; t=\frac{1}{5}$

Now the root are $-\frac{6}{5}$ and $\frac{1}{5}$, the value $-\frac{6}{5}$ can’t be used as negative value can’t have square root without forming complex number therefore, the positive value$t=\frac{1}{5}$ is taken from the equation.

Replace t by $\sqrt{X}$ we get

$\sqrt{X}=\frac{1}{5} ; X=\frac{1}{25}$

Therefore, the number is $X=\frac{1}{25}$.