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Difference of 2 numbers is 1.Difference of their reciprocals is 1/20.Which are the numbers?

Dear Student,

Refer the similar link:
https://www.meritnation.com/ask-answer/question/q1-the-difference-of-two-numbers-is-5-and-the-difference-of/quadratic-equations/3203500  

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Let the numbers be x and y.
Now, According to question :
x  -  y  =  1               (...1)
and                                       
1  -  1  =    1             (...2)
x     y       20

From (...1)
x  =  1  +  y

Now, put the value of x in (...2), we get:
1  -  1  =    1  
x     y       20

     1      -  1  =    1 
1  +  y      y       20

y  +  1  -  y   =   1 
( 1  +  y )y      20

     1        =    1 
y  +  y2​         20

y2​  +  y  =  20

y2​  +  y  -  20  =  0

y2​  +  5y  -  4y  -  20  =  0
 
y ( y  +  5 )  -4 (y  +  5 ) = 0

( y  -  4 ) ( y  +  5 )

y  =  4 and -5

So, we take positive numbers
So,  
y = 4  

Now put the value of y in (...1)
x  -  y  =  1
x  -  4  =  1
x  =  1  +  4
x  =  5

Now the numbers are 5 and 4
 
Thanks and good morning



 
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