Remember that the quadratic formula is: .
stands for the coefficient of the first term, the one associated with the
,
stands for the coefficient of the second term, the one associated with
, and
stands for the value of the constant.
In , our a-value is 1, our b-value is also 1, and our c-value is also 1.
Thus, when we plug in our values into our formula, we get the answer:
Simplifying this answer using , we get our final answer of:
Answer:
1. Equilibrium solution: y= -3
2. Equilibrium solution y= ±1.414
Step-by-step explanation:
Thinking process:
The equilibrium solution can only be derived when
1. Let's look at the first equation:
equating to the expression
gives
y + 3 = 0
y = -3
Therefore, the equilibrium solution occurs at y = -3
2. Let's look at the second solution:
dividing each side by (t²-1) gives
1/(t²-1) = (y²-2)/ (y²-4)
factorizing the right hand side gives:
at equilibrium: , then
y² - 2 = 0
solving for y gives y = ±√2
= ±1.414