Answer :
Answer
what equation represents the situation?x(x+1)=182
what are the 2 numbers? -13 and -14
Step-by-step explanation:
Using a system of equations, it is found that the equation that represents the situation is:
n(n - 1) = 182.
The numbers are -13 and -14.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, since the integers are consecutive, the variables are n and n - 1.
The product is of 182, hence:
n(n - 1) = 182.
Then:
n² - n - 182 = 0.
Which is a quadratic equation with coefficients a = 1, b = -1, c = -182. Hence the solutions are found as follows:
[tex]\Delta = (-1)^2 - 4(1)(-182) = 729[/tex]
[tex]x_1 = \frac{1 + \sqrt{729}}{2} = 14[/tex]
[tex]x_2 = \frac{1 - \sqrt{729}}{2} = -13[/tex]
We take the negative root, hence the numbers are -13 and -14.
More can be learned about a system of equations at https://brainly.com/question/24342899
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