SOLUTION: The sum of two numbers is 2. Three times the sum of their reciprocals is 8. What are the numbers?

Hi

Let x and (2-x)represent the two numbers

3[1/x + 1/(2-x)] = 8  

  3 /x + 3/(2-x) = 8 Multiplying each side of the equation by x(2-x)

3(2-x) + 3x = 8x(2-x)

6 - 3x + 3x = 8x(2-x)

 6 = 16x - 8x^2

8x^2 -16x + 6 = 0

4x^2 - 8x + 3 = 0





  x = 1.5 and x = .5

 CHECKING our Anwer

 3[2/3 + 2] = 2 + 6 = 8