Question

If x and y are natural numbers, how many ordered pairs (x,y) are solution of the equation 1/x + 1/y = 1/13?

Answer 1

3 ordered pairs : (26,26) and (13*14,14) (14,13*14)

Given:

If x and y are natural numbers.

To Find:

Number of order pairs (x, y) possible for the solution of the equation 1/x + 1/y = 1/13.

Solution:

1/x +1/y = 1/13

=> (x + y)/x*y = 1/13

• Since x and y are natural numbers, x*y should be a factor of 13,

        that means either x = 13a or y = 13b

let us assume x = 13a, y = b

then,

13a+b/13ab = 1/13

b = 13a/(a-1)

For b to be natural number,

(a-1) = 1 or (a -1) = 13

hence, x =26, y = 26

or, x = 13*14, y = 14

Similarly, when y is multiple of 13

x=14, y = 13*14

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Answer 2

Answer:

The possible ordered pairs that are the solution of the equation

1/x + 1/y = 1/13 are : (26,26) and (13*14,14) (14,13*14).

Step-by-step explanation:

Information provided :

If × and y are natural numbers.

To Find:

Number of order pairs (×, y) possible for the solution of the equation 1/x + 1/ = 1/13.

Solution:

1/x +1/y = 1/13

=> (x + y)/x*y = 1/13

As natural numbers, x and y, x*y should be a factor of 13.

So we can say that either x = 13a or y = 13b

Lets see what happens if we assume x = 13a, y = b

then,

13a+b/13ab = 1/13

b= 13a/(a-1)

For b to be natural number,

(a-1) = 1 or

(a -1) = 13

hence, x=26, y = 26

or, x = 13*14, y = 14

Similarly, when y is multiple of 13

x=14, y = 13*14

Therefore, according to our calculations, the possible solutions are (26,26) and (13*14, 14) (14,13*14).  

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