Let the two consecutive positive integers be x and x + 1.
According to the problem, the product of these integers can be expressed as:
x(x + 1)
Their sum can be expressed as:
x + (x + 1) = 2x + 1
The problem states that the product is 55 more than their sum, so we can set up the equation:
x(x + 1) = (2x + 1) + 55
This simplifies to:
x(x + 1) = 2x + 56
Now, let’s rearrange this equation:
x^2 + x – 2x – 56 = 0
x^2 – x – 56 = 0
Next, we can factor this quadratic equation:
(x – 8)(x + 7) = 0
Setting each factor equal to zero gives:
- x – 8 = 0 → x = 8
- x + 7 = 0 → x = -7
Since we are looking for positive integers, we disregard x = -7.
Thus, the two consecutive positive integers are:
x = 8 and x + 1 = 9.
In conclusion, the two consecutive positive integers are 8 and 9.