Question

The sum of a number and its reciprocal is `2 1/20` The number is  

(a) `5/4  or  4/5`                        (b)`4/3  or  3/4` 

(c) `5/6  or  6/5`                         (d) `1/6  or  6`

Answer 1

(a)` 5/4  or  4/5` 

Let the required number be x. 

According to the question  

`x+1/x=41/20` 

⇒`(x^2+1)/x=41/20` 

⇒`20x^2-41x+20=0` 

⇒`20x^2-25x-16x+20=0` 

⇒`5x(4x-5)-4(4x-5)=0` 

⇒`(4x-5) (5x-4)=0` 

⇒`x=5/4   or  x=4/5`