Question

The sum of two numbers is 18. The sum of their reciprocals is 1/3. find the numbers

Answer 1

Let the two numbers be,

x+y=18........(1)

1/x +1/y =1/3...... (2)

Solving eqn 2

x+y/xy=1/3

18/xy=1/3

xy=6........(3)

x=6/y

Now , in eqn (1)

x+y=18

6/y + y=18

y^2 - 18y + 6=0.......(4)

Solve equation 4

You'll get 'y' and using 'y' calculate 'x'.