Question

The sum of the numbers is 15 and the sum of their reciprocals is 3/10. Formulate the quadratic equation to find the two numbers.​

Answer 1

Answer:

5 and 10 are the two numbers

Step-by-step explanation:

x and 15-x be the numbers

so 1/x + 1/(15-x) = 3/10

=> (15-x+x)/x(15-x) = 3/10

=> 15/(15x-x^2) = 3/10

=> 15×10/3 = 15x-x^2

=> 50 = 15x-x^2

=> x^2 - 15x + 50 = 0

=> x^2 - 10x - 5x + 50 = 0

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

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

Therfore,

x = 10 or x = 5

=> 15-x = 5 or 15-x = 10