The difference of two number is 5 and the difference of their reciprocal is 1/10 find the number.

The difference of two number is 5 and the difference of their reciproc

1.	The difference of two number is 5 and the difference of their reciprocal is 1/10 find the number.
Answer» Let the first number be x{tex}\\therefore {/tex}\xa0Second number = x + 5Now according to the question{tex}\\frac { 1 } { x } - \\frac { 1 } { x + 5 } = \\frac { 1 } { 10 }{/tex}{tex}\\Rightarrow \\quad \\frac { x + 5 - x } { x ( x + 5 ) } = \\frac { 1 } { 10 }{/tex}{tex}\\Rightarrow \\quad 50 = x ^ { 2 } + 5 x{/tex}{tex}\\Rightarrow \\quad x ^ { 2 } + 5 x - 50 = 0{/tex}{tex}\\Rightarrow \\quad x ^ { 2 } + 10 x - 5 x - 50 = 0{/tex}{tex}\\Rightarrow x ( x + 10 ) - 5 ( x + 10 ) = 0{/tex}{tex}\\Rightarrow \\quad ( x + 10 ) ( x - 5 ) = 0{/tex}x = 5 ,- 10 rejectedThe numbers = 5 and 10.