The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
Let X = first integer
X + 1 is the second.
------------------
X*(X+1) = X + X+ 1 + 11
Solve for X and X+1. That's a quadratic equation.
To solve this problem, let's represent the two consecutive positive integers as x and x+1.
According to the given information, the product of these two integers is 11 more than their sum. We can express this as the following equation:
x(x+1) = x + (x+1) + 11
Let's simplify this equation:
x^2 + x = 2x + 12
Rearrange the equation by subtracting 2x and 12 from both sides:
x^2 - x - 12 = 0
Now, we have a quadratic equation. To solve for x, we can factor this equation:
(x - 4)(x + 3) = 0
Setting each factor equal to zero:
x - 4 = 0 --> x = 4
x + 3 = 0 --> x = -3
Since we are looking for positive integers, we can discard the solution x = -3.
Therefore, the two consecutive positive integers are x = 4 and x+1 = 4+1 = 5.
Hence, the two integers are 4 and 5.