Question

The sum of two numbers is 15, and their product is 16. What is the sum of the reciprocals of the two numbers? Express your answer as a common fraction.

Answer 1

Answer:

The sum of the reciprocal of two numbers are  

  $\frac{1}{x} + \frac{1}{y}= \frac{15}{16}$

Step-by-step explanation:

Step(i):-

Let  x , y  are  two numbers

Given data the sum of two numbers = 15

         x + y = 15 ...(i)

The product of two numbers = 16

         x y = 16  ...(ii)

we know that

(x-y)² = (x + y)² - 4 x y

         = (15)²- 4(16)

        = 225 - 64

        = 161

x-y = 12.68 ≅13  ...(iii)

Step(ii):-

We have

                  x + y = 15  ...(a)

                  x -y   = 13  ...(b)

Solving (a) and (b)

                  2x = 27.68

                  x = 13.84

Substitute x = 13.84 in equation (i)

                x + y = 15

              13.84 + y = 15

                         y = 15 - 13.84

                        y = 1.16

Step(iii):-

The positive numbers are x = 13.84 and y = 1.16

The sum of the reciprocal of two numbers are

                      $\frac{1}{x} + \frac{1}{y} = \frac{1}{13.84} + \frac{1}{1.16}$

                                 = $\frac{15}{16}$

Conclusion:-

The sum of the reciprocal of two numbers are  

  $\frac{1}{x} + \frac{1}{y}= \frac{15}{16}$