Question

Two numbers differ by 3. The sum of their reciprocals is 7/10. Find the numbers.​

Answer 1

Explanation:

let the number be x and y

then from first condition

x - y = 3

x = y + 3

again from second condition

1/ x + 1/ y = 7 / 10

1/(y+3) + 1/y = 7 / 10

y + (y+3) = 7/ 10 y(y+3)

10(2y + 3) = 7y² + 21y

or, 7y² + 21y - 20y - 30 = 0

or, 7y² + y - 30 = 0

0r, 7y² - 14y + 15y - 30 = 0

or, ( y-2) ( 7y + 15) = 0

either

y = 2 0r -15/7

if two number are natural then two is only valid number

again from first condition

x - y =3

x - 2 = 3

x =5