Question

The sum of a number and its reciprocal is $2\frac{1}{30}$. Find the number.

Answer 1

Let the one number be 'x'
So, its reciprocal will be $\frac{1}{x}$
Now, according to the question.
$x+\frac{1}{x}=2\frac{1}{30}=\frac{61}{30}\frac{(x²+1)}{x}=\frac{61}{30}30x^2+30=61x30x^2-61x+30=030x^2-36x-25x+30=06x(5x-6)-5(5x-6)=0(6x-5)(5x-6)=06x=5or5x=6x=\frac{5}{6}orx=\frac{6}{5}$

So, the numbers are $\frac{5}{6}$ and $\frac{6}{5}$