Let the two numbers be x and y,
Given that,
x - y = 4
x = y + 4 .....(i)
and
\(\frac 1y - \frac 1x = \frac 4{21}\)
\(\frac {x - y}{xy} = \frac 4{21}\)
\(\frac 4{xy} = \frac 4{21}\)
\(xy = 21\)
From (i),
(y + 4)y = 21
y2 + 4y - 21 = 0
y2 + 7y - 3y - 21 = 0
y(y + 7) - 3(y + 7) = 0
(y - 3) (y + 7) = 0
y = 3, -7
So, when y = 3; x = y + 4 = 7
Or, when y = -7; x = y + 4 = -3
