Question

The difference of two natural numbers is 5 and then the difference of their reciprocals is 110. Find the numbers. ​

Answer 1

Answer:

x-y = 6 => x = y+6

1/x - 1/y = 110 => y-x/xy = 110

y-(y+6)/(y+6)y = 110

-6/y²+6y = 110

110y² + 660y +6 = 0

cannot be factorised

Answer 2

x-y=5. - eq 1

1/x-1/y=110

(y-x)/xy=110

y-x=110xy

y-(y+5)=110(y+5)y. (from eq 1)

y-y-5=110(y square+5y)

-5=5×22(y square + 5y)

-1=22y square+110y

22y square+110y+1=0

HENCE , WE CANT SOLVE THE EQUATION

if we solve also,we wii not get natural roots