find x if ac=2x-1 and ae=x2-2
What is relation between AC and AE?
Also, online exponents are indicated by "^", x^2 = x squared.
find x if segment AC=2x-1 and segment AE=x^x-2
8=8
To find the value of x, we need to set up an equation using the given information.
We are given that ac = 2x - 1 and ae = x^2 - 2.
Since "ac" and "ae" involve the same variables (a and c, and a and e, respectively), we can equate them to find a relationship between x and x^2.
ac = ae
(2x - 1) = (x^2 - 2)
Now, we can solve this equation to find the value of x.
Rearrange the equation to bring all terms to one side:
x^2 - 2 - (2x - 1) = 0
Simplify:
x^2 - 2 - 2x + 1 = 0
Combine like terms:
x^2 - 2x - 1 = 0
This is now a quadratic equation. We can solve it using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -2, and c = -1:
x = (-(-2) ± √((-2)^2 - 4(1)(-1))) / (2(1))
Simplifying further:
x = (2 ± √(4 + 4)) / 2
x = (2 ± √(8)) / 2
x = (2 ± 2√2) / 2
Simplifying the expression:
x = 1 ± √2
Therefore, the two possible values of x are 1 + √2 and 1 - √2.