find x if segment AC=2x-1 and segmentAE=x^2-2 how do I find x

How AC is related to AE, are they equal?

If yes, then you have to solve this way:
AC=AE
2x-1=x^2-2, then solve for x
x=1

how di find perimeter of the triangle in terms of x one side is 5, secod side is 4x, and the third side is x-3 will u please help me any one. thanks

To find the value of x, we can use the given information about the segments AC and AE.

1. Given segment AC = 2x - 1
2. Given segment AE = x^2 - 2

Since segment AC and segment AE represent the same line segment, we can equate them:
AC = AE

Substituting the given expressions:
2x - 1 = x^2 - 2

Now, we have a quadratic equation. Let's rearrange it to get it into standard form:
x^2 - 2 - 2x + 1 = 0
x^2 - 2x - 1 = 0

To solve this quadratic equation, you can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation x^2 - 2x - 1 = 0:
a = 1, b = -2, c = -1

Substituting the values into the quadratic formula:
x = (-(-2) ± √((-2)^2 - 4(1)(-1))) / (2(1))
x = (2 ± √(4 + 4)) / 2
x = (2 ± √8) / 2

Simplifying further:
x = (2 ± 2√2) / 2
x = 1 ± √2

Therefore, the possible values for x are 1 + √2 and 1 - √2.