Question

If the product of two consecutive positive integers
is 650, then the sum of the two integers is​

Answer 1

Answer:

Two consecutive positive integers whose product is 650 are 25 and 26. Done.

Answer 2

Required Answer :

The sum of the two integers = 51

Given :

• Product of two consecutive positive integers = 650

To find :

• The sum of the two integers

Solution :

Let the two positive integers be x, x + 1

• First number = x
• Second number = x + 1

According to the question,

⇒ First number × Second number = 650

⇒ x(x + 1) = 650

⇒ x² + x = 650

⇒ x² + x - 650 = 0

A quadratic equation is formed whose product is - 650.

⇒ x² + 26x - 25x - 650 = 0

⇒ x(x + 26) - 25(x + 26) = 0

⇒ (x - 25)(x + 26) = 0

⇒ (x - 25) = 0 or (x + 26) = 0

⇒ x = 25 or x = - 26

The value of x = - 26 will get rejected. Because it is mentioned in the question that the numbers are positive integers.

So, the value of x = 25

Substituting the value of 'x' in the numbers which we've assumed :-

⇒ First number = x

⇒ First number = 25

⇒ Second number = x + 1

⇒ Second number = 25 + 1

⇒ Second number = 26

The sum of the two positive integers :-

⇒ First number + Second number

⇒ 25 + 26

⇒ 51