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.
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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.