Question

The sum of a number and its reciprocal is `2 1/30` Find the number. 

Answer 1

Let the required number be x.
According to the given condition, 

`x+1/x=2 1/30` 

⇒`x^2+1/x=61/30` 

⇒ `30x^2+30=61x` 

⇒`30x^2-61x+30=0` 

⇒`30x^2-36x-25+30=0` 

⇒`6x(5x-6)-5(5x-6=0)` 

⇒`(5x-6) (6x-5)=0` 

⇒`5x-6=0  or  x=5/6` 

⇒`x=6/5  or  x=5/6` 

Hence, the required number is` 5/6  or  6/5`