the sum of two natural numbers is 8 and the sum of their reciprocal is 8/15 . find the numbers
Answers
Answered by
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
Similar questions