Question

the difference between two number is 4 . if the difference of their reciprocal is 4/ 21 . find the numbers

Answer 1

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Answer 2

heyy mate here is your Answer

Let the two numbers be x and y

ATP
x-y = 4................... (i)
1/x -1/y = 4/21
y-x/xy = 4/21
21 (y-x) = 4xy
21x - 21y = 4xy........... (ii)

Now in eq.( i )
x= 4+y

Substituting the value of x in eq.( ii )

21x -21y = 4xy
21 ( 4+y) - 21y = 4y (4+y)
84 + 21y -21y = 16y + 4y^2
84 = 4y^2+16y
4y^2 +16y -84 =0
4 (y^2+ 4y -21)=0
y^2 + 4y -21 = 0/4
y^2 +(7-3)y -21=0
y^2 +7y -3y -21=0
y (y+7) -3 (y+7)=0
(y+7)(y-3)=0
y=3

x-y=4
x-3=4
x=4+3
x=7


Hence the two numbers are 3 and 7