Question

The sum of two numbers is 15. If the sum of their reciprocals is 3/10, find the two numbers.

Answer 1

Answer:

let one number be x, and the other be y,

acc. to question,

 x + y = 15

y = 15 - x .....(1)

now ,  

    1/x + 1/y = 3/10

   1/x + 1/15-x = 3/10      ( put value of y .. from (1) )

15 - x + x / 15x - x^2 = 3/10

=>  150 = 45x - 3x^2

=>   3x^2 - 45x + 150 = 0

divide throughout by 3, we get,

 x^2 - 15x + 50 = 0

x^2 -(10+5)x + 50 = 0

x(x-10) -5(x-10) = 0

(x-5) (x-10)

x=5,10

now,

when , x=5

numbers=> 5,10

when, x=10

numbers=>10,5

Step-by-step explanation:

Answer 2

Step-by-step explanation:

the numbers are 5 and 10.

see the attachment for the solution.

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