Question

The sum of two natural numbers is 9 and the sum of their reciprocals is9/20
Find the numbers.
​

Answer 1

Answer:

No real value of x is possible. so question is incorrect

Step-by-step explanation:

Given,

Sum of two numbers = 9

Sum of their reciprocal = 9 / 20

To find: The numbers

Solution:

Let the one number be x.

Then another number = ( 9 - x)

Then the equation formed will be,

$</p><p>\begin{gathered}\dfrac{1}{x} + \dfrac{1}{(9-x)} = \dfrac{9}{20}\\\\\dfrac{(9-x)+x}{x(9-x)} = \dfrac{9}{12}\\\\12 \times 9 = 9 (9x -x^2)\\\\108 = 18x - 9x^2\\\\12 = 2x - x^2\\\\x^2 - 2x + 12 = 0\\\\\end{gathered} </p><p>x$

1

+

(9−x)

1

=

20

9

x(9−x)

(9−x)+x

=

12

9

12×9=9(9x−x

2

)

108=18x−9x

2

12=2x−x

2

x

2

−2x+12=0

No real value of x is possible.