- sum of a number and its
square root is 6
Answers
Answer:
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Answer:
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}.
25
1
.
Hence, the sum is X+\sqrt{X}=\frac{6}{25}X+
X
=
25
6
Now let us take \sqrt{X}=t
X
=t we get the equation of X+\sqrt{X}=\frac{6}{25} \text { as } t^{2}+t-\frac{6}{25}=0X+
X
=
25
6
as t
2
+t−
25
6
=0
Simplifying the equation we get 25 t^{2}+25 t-625t
2
+25t−6 . Let us find the roots of the equation we get
5 t(5 t+6)-1(5 t+6)=05t(5t+6)−1(5t+6)=0
(5t+6)(5t-1)=0
t=-\frac{6}{5} ; t=\frac{1}{5}t=−
5
6
;t=
5
1
Now the root are -\frac{6}{5}−
5
6
and \frac{1}{5}
5
1
, the value -\frac{6}{5}−
5
6
can’t be used as negative value can’t have square root without forming complex number therefore, the positive valuet=\frac{1}{5}t=
5
1
is taken from the equation.
Replace t by \sqrt{X}
X
we get
\sqrt{X}=\frac{1}{5} ; X=\frac{1}{25}
X
=
5
1
;X=
25
1
Therefore, the number is X=\frac{1}{25}X=
25
1
.