Answer:
![\huge\boxed{5, 6, 7}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B5%2C%206%2C%207%7D)
Step-by-step explanation:
In order to find the 3 consecutive digits here, we need to note that consecutive numbers are numbers that appear as the number right above each other.
For example: 2, 3, 4 are consecutive, as are -10, -9, -8.
We can assign the first term a variable, let's do x. Since we know the next two terms are consecutive, we can define them with
and
.
![x, (x+1), (x+2)](https://tex.z-dn.net/?f=x%2C%20%28x%2B1%29%2C%20%28x%2B2%29)
We also know that the first number squared, increased by the last, is 32. This can be modeled by the equation
![x^2 + (x+2) = 32](https://tex.z-dn.net/?f=x%5E2%20%2B%20%28x%2B2%29%20%3D%2032)
Let's solve for x in that equation by using the XBOX Method in quadratics.
- <em>The product of the two roots will be c (-30) and their sum will be b (1)</em>.
- <em>Zeroes of the function: </em>
Now that we know two values of x that might work, we need to plug them into our equation to test if they actually do work.
5
![5^2 + (5+2) = 32\\\\ 25 + 7 = 32 \ \checkmark](https://tex.z-dn.net/?f=5%5E2%20%2B%20%285%2B2%29%20%3D%2032%5C%5C%5C%5C%2025%20%2B%207%20%3D%2032%20%5C%20%5Ccheckmark)
-6
![-6^2 + (-6+2) = 32 \\\\ -36 + -4 = 32 \ \times](https://tex.z-dn.net/?f=-6%5E2%20%2B%20%28-6%2B2%29%20%3D%2032%20%5C%5C%5C%5C%20-36%20%2B%20-4%20%3D%2032%20%5C%20%5Ctimes)
We can see here that -6 won't work as it doesn't satisfy our equation. However, 5 does work. That means our first number is 5, making our next two numbers 6 and 7.
Hence - 5, 6, 7.
Hope this helped!