Question

Solve the problem.The product of two consecutive integers is 11 more than their sum. Find theintegers.O 4,5 or -3, -2O 4,5O 3, 4 or -3, -20 -3, -2

Answer 1

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:

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

In this case, we have:

a = 1

b = -1

c = -12

Then, x is given by:

$\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1} \\ \\ x=\frac{1\pm\sqrt[]{1+48}}{2}=\frac{1\pm\sqrt[]{49}}{2}=\frac{1\pm7}{2} \\ \\ x_1=\frac{8}{2}=4\text{ }\Rightarrow x_1+1=5 \\ \\ x_2=-\frac{6}{2}=-3\text{ }\Rightarrow x_1+1=-2 \end{gathered}$

Therefore, the integers can be:

4, 5 or -3, -2