Answer:
{-1, 2}
Step-by-step explanation:
The quantity x + 1 changes sign at x = -1; equivalently, x + 1 = 0 when x = -1.
If x = -1, then |x+1|+|x−2|=3 becomes |-1 + 1| + |-1 −2|=3, which is TRUE. So x = -1 is a solution.
If x = 2, then we have the equation |2 + 1| + |2 − 2|=3, or |2 + 1| = 3, which is TRUE. So x = 2 is also a solution.
You multiply the two together
x times x equals x squared ( x^2) the x times 2 which equals 2x, then multiply the 3 and x to get 3x and multiply 3 times 2 = 6
so now your problem looks like x[tex] x^{2} + 2x +3x +6 ( now combine like terms) which gives you x^{2} +5x +6, and thats the answer
Answer:
![y" + 2y' + 2y = 0](https://tex.z-dn.net/?f=y%22%20%2B%202y%27%20%2B%202y%20%3D%200)
Step-by-step explanation:
Given
![y=c_1e^{-x}cosx+c_2e^{-x}sinx](https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B-x%7Dcosx%2Bc_2e%5E%7B-x%7Dsinx)
Required
Determine a homogeneous linear differential equation
Rewrite the expression as:
![y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)](https://tex.z-dn.net/?f=y%3Dc_1e%5E%7B%5Calpha%20x%7Dcos%28%5Cbeta%20x%29%2Bc_2e%5E%7B%5Calpha%20x%7Dsin%28%5Cbeta%20x%29)
Where
and ![\beta = 1](https://tex.z-dn.net/?f=%5Cbeta%20%3D%201)
For a homogeneous linear differential equation, the repeated value m is given as:
![m = \alpha \± \beta i](https://tex.z-dn.net/?f=m%20%3D%20%5Calpha%20%5C%C2%B1%20%5Cbeta%20i)
Substitute values for
and ![\beta](https://tex.z-dn.net/?f=%5Cbeta)
![m = -1 \± 1*i](https://tex.z-dn.net/?f=m%20%3D%20-1%20%5C%C2%B1%201%2Ai)
![m = -1 \± i](https://tex.z-dn.net/?f=m%20%3D%20-1%20%5C%C2%B1%20i)
Add 1 to both sides
![m +1= 1 -1 \± i](https://tex.z-dn.net/?f=m%20%2B1%3D%201%20-1%20%5C%C2%B1%20i)
![m +1= \± i](https://tex.z-dn.net/?f=m%20%2B1%3D%20%5C%C2%B1%20i)
Square both sides
![(m +1)^2= (\± i)^2](https://tex.z-dn.net/?f=%28m%20%2B1%29%5E2%3D%20%28%5C%C2%B1%20i%29%5E2)
![m^2 + m + m + 1 = i^2](https://tex.z-dn.net/?f=m%5E2%20%2B%20m%20%2B%20m%20%2B%201%20%3D%20i%5E2)
![m^2 + 2m + 1 = i^2](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%201%20%3D%20i%5E2)
In complex numbers:
![i^2 = -1](https://tex.z-dn.net/?f=i%5E2%20%3D%20-1)
So, the expression becomes:
![m^2 + 2m + 1 = -1](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%201%20%3D%20-1)
Add 1 to both sides
![m^2 + 2m + 1 +1= -1+1](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%201%20%2B1%3D%20-1%2B1)
![m^2 + 2m + 2= 0](https://tex.z-dn.net/?f=m%5E2%20%2B%202m%20%2B%202%3D%200)
This corresponds to the homogeneous linear differential equation
![y" + 2y' + 2y = 0](https://tex.z-dn.net/?f=y%22%20%2B%202y%27%20%2B%202y%20%3D%200)
I think the answer should be