Question

The difference of the two number is 4 and the difference between their recipocal is 4/21 .Find the number .

Answer 1

Let the numbers be x and y
A/q
x-y = 4(given) (i)
Difference of reciprocal is 4/21
So, 1/x - 1/y = 4/21
Or, y-x/xy = 4/21
Or, 21y -21x = 4xy (ii)
From eqn (i) we get x-y =4
Or, x = 4+y (iii)
Putting the value of x in eqn I
21y - 21x = 4xy
21y - 21(4-y) = 4(4-y) y
21y - 84 - 21y = 16y+4ysquare
-84 = 16y + 4y square
4y square +16y + 84 = 0
4y square + 28y-12y = 0
4y(y+7) -12(y+7) = 0
(4y-12) (y+7)
Or, y = 3 and -7
By neglecting negative number we get y = 3
Putting the value of y in equation (iii)
x=4+y
Or, x= 4+3
Or, x=7
So required numbers are 3 & 7