Question

the sum of two natural numbers is 8 and the sum of their reciprocal is 8/15 . find the numbers​

Answer 1

Let the two numbers be A , B

A + B = 8 ----> (1) => A = 8 - B ------(2)

1/A + 1/B = 8/15

=> B + A / AB = 8/15

=> 8/AB = 8/15 { ∵ From eq(1) }

=> 1/AB = 1/15

=> AB = 15 => 8 - B(B) = 15

=> 8B - B^2 = 15 => -B^2 + 8B - 15 = 0

=> -B^2 -5B - 3B - 15 = 0

=> -B ( B + 5 )-3 ( B + 5 ) = 0

=> ( B + 5 )( -B- 3 ) = 0

=> B = -5 (or) B = -3

when B = -5 ,

A = 8 - (-5) = 13

When B = -3 ,

A = 8-(-3) = 11

∴ A = 11 (or) A = 13 ; B = -5 (or) B = -3