Question

the sum of 2 number is 9 its reciprocal is 1/2 find the number

Answer 1

Let the first number be a

Second number = 9 - a

According to question,

1/a + 1/ ( 9 - a) = 1/2

=> ( 9-a + a) / a(9 - a) = 1/2

=> 9 / 9a - a^2 = 1/2

=> 18 = 9a - a^2

=> a^2 - 9a + 18 = 0

=> a^2 - 6a - 3a + 18 = 0

=> a ( a - 6) - 3(a-6) = 0

=> (a-6)(a-3) = 0

First number = 6

Second number = 3

Or

First number = 3

Second number = 6