Let x and x + 1 be two consecutive integer numbers. Then, the sentences in this question can be written as:
x(x+1) = 11 + x + x+1
Now, we can develop this equation to find:
x(x+1) = 11 + x + x+1
x² + x = 12 + 2x
x² + x - 2x - 12 = 12 + 2x - 2x - 12
x² - x - 12 = 0
Remember we can solve the equation in the form ax² + bx + c = 0 by using the following formula:
In this case, we have:
a = 1
b = -1
c = -12
Then, x is given by:
Therefore, the integers can be:
4, 5 or -3, -2