[(x^2-1)/(x)]^2 - [(x^2-1)/(x)] - 2 = 0
I let u = (x^2-1)/(x)
so I get
u = -1 , 2
my problem is when i plug it back in
x^2 - 1 x^2 - 1
-------- = - 1 ----------- = 2
x x
How do I solve for X?
Sorry the formatting messed up
For simplicity, I just want to find out how to find X after I find u
if you know u
ux=x^2-1
x^2-ux-1=0
use the quadratic formula.
To solve for x, you need to solve for the expression u that you substituted, which is equal to (x^2-1)/x. Let's solve for x step by step.
1. Start with the equation: u = (x^2-1)/x.
2. Multiply both sides of the equation by x to eliminate the denominator:
u * x = x * (x^2-1)/x.
This simplifies to:
u * x = x^2 - 1.
3. Rearrange the equation to isolate x^2:
x^2 = u * x + 1.
4. Rewrite the equation as a quadratic equation by subtracting u * x and 1 from both sides:
x^2 - u * x - 1 = 0.
Now, you have a quadratic equation in terms of x. To solve this equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, the quadratic equation is:
x^2 - u * x - 1 = 0.
Compare it with the general form:
ax^2 + bx + c = 0.
From the quadratic equation, you can identify the coefficients as follows:
a = 1, b = -u, c = -1.
Substitute these values into the quadratic formula and solve for x using both possible values of u that you obtained:
For u = -1:
x = (-(-1) ± √((-1)^2 - 4(1)(-1))) / (2(1)).
Simplifying further,
x = (1 ± √(1 + 4)) / 2
x = (1 ± √5) / 2
For u = 2:
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
x = 1 ± √2
Therefore, the solutions for x are:
For u = -1:
x = (1 + √5) / 2 or x = (1 - √5) / 2
For u = 2:
x = 1 + √2 or x = 1 - √2.