Question

The difference of two no. is 4 and the difference of their reciprocal is 4/21( four upon twenty one ) . Find the no.

Answer 1

Let the numbers be x and y.
x-y= 4 ...(i)
1/y-1/x=4/21 ...(ii)
From (i) we have-
x=4+y
Putting value of x in (ii)-
1/y-1/4+y=4/21
or 4+y-y/4y+y2=4/21
or 4=(16y+4y2)/21
or 84=4y2+16y
or 4y2+16y-84=0
or y2+4y-21=0
or y2+7y-3y-21=0
or y(y+7)-3(y+7)=0
or (y-3)(y+7)=0
Therefore,
y= 3 and -7
And,
x= 7 and -3 (respectively)
Hope it helps! 

Answer 2

Let a and b be the two numbers. According to question, a - b = 4 and   .....(since we assume that a > b) Thus, we have   When b = -7, a - (-7) = 4 i.e. a = 4 - 7 = -3 When b = 3, a = 4 + 3 = 7  Hope it helps
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