Question

the difference of two number is 5 and the difference of their reciprocal is 1 by 10 find the numbers

Answer 1

let
x-y=5
x-1/y= 1/10
solve this
xy-1=y/10
10xy-10=y
10xy-y=10
10y(x-1) =10
10y(5+y) =10
50y+10y²=10
10y²+50y-10=0
solve it you got your answer

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

First number be p

Second number be p - 5

Here,

p > (p - 5)

= 1/p < 1/p - 5

So,

= 1/p - 5 > 1/p

Situation,

1/p - 5 - 1/p = 1/10

p - (p - 5)/(p - 5)p = 1/10

5/(p - 5)p = 1/10

(p - 5)p = 50

p² - 5p - 50 = 0

p² - 10p + 5p - 50 = 0

p(p - 10) + 5(p - 10) = 0

(p - 10)(p + 5) = 0

p - 10 = 0 or p + 5 = 0

p = 10, -5 (Negative value is not acceptable)

p = 10

First Number = p = 10

Second Number

= p - 5

= 10 - 5

= 5