Question

The product of two positive integers is twice their sum, the product is also equal to six times the difference between the two integers. the sum of these integers is​

Answer 1

Answer:

9

Step-by-step explanation:

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Answer 2

The sum of the integers is​ 6

Given:

The product of two positive integers is twice their sum

The product is also equal to six times the difference between the two integers

To find:

The sum of these integers is​

Solution:

Let x and y be the two positive integers

Given that the product of two positive integers is twice their sum

⇒ xy = 2(x+y) ----(1)

The product is also equal to six times the difference between the two integers

⇒ xy = 6(x - y) -----(2)

From (1) and (2)

⇒ 2(x+y)  =  6(x - y)  

⇒ 2x + 2y = 6x - 6y

⇒  8y = 4x

⇒  x = 2y

Substitute for x in the first equation:

⇒  (2y)y = 2(2y+y)  

⇒   2y² = 6y

⇒   y² = 3y

⇒  y(y - 3) = 0

⇒ y = 0  or   y = 3

⇒ When y = 0 ⇒ x = 2(0) = 0

⇒ When y = 3 ⇒ x = 2(3)  = 6  

As the integers are positive they must be 3 and 6.

Therefore, x = 6 and y = 3

⇒ The sum of the integers x+y = 6+3 = 9

The sum of the integers is​ 6

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