Question

divide 15 into 2 parts such that the sum of their reciprocals is 3/10

Answer 1

Hey,
Thanks for asking this question.

Lets suppose that one of the no is x.
Since the sum of both numbers is 15
So the other no is (15-x).

sum of their reciprocal = 3/10
=> 1/x + 1/(15-x) = 3/10

=> {(15-x) + x} / (x)×(15-x) = 3/10
=> 15×10 = 3 × (x)(15-x)
=> 150 = 45x - 3x^2
=> 3x^2 - 45x + 150 = 0
=> x^2 - 15x + 50 = 0 ( dividing full equation with 3)

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

●So if one number is 5,the other number is 15-5,that is 10.


●●●Hope my answer helped.