A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.

The required two integers are 7 and 14

This is a question on word problems leading to the simultaneous equation:

Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1

Also, if the sum of the reciprocals of the two positive integers is 3/14, then:

..........2

Substitute equation 1 into 2

Find the LCM of 2y and y

Substitute y = 7 into equation 1:

Recall that x = 2y

Hence the required two integers are 7 and 14.

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The integers are 7 and 14.

Step-by-step explanation:

y = 2x

1/y + 1/x = 3/14

1/(2x) + 1/x 3/14

1/(2x) + 2/(2x) = 3/14

3/(2x) = 3/14

1/2x = 1/14

2x = 14

x = 7

y = 2x = 2(7) = 14

The integers are 7 and 14.

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