I'm not sure how to begin attacking this one.

Given the equation $\displaystyle 4x^2 - 4xy + 1 - y^2 = 0$

use the Quadratic Formula to solve for

(a) x in terms of y (b) y in terms of x.

Can I get a hint?

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- Jul 10th 2007, 02:33 PMearacheflOne more equation
I'm not sure how to begin attacking this one.

Given the equation $\displaystyle 4x^2 - 4xy + 1 - y^2 = 0$

use the Quadratic Formula to solve for

(a) x in terms of y (b) y in terms of x.

Can I get a hint? - Jul 10th 2007, 03:08 PMThePerfectHacker
- Jul 10th 2007, 03:27 PMearachefl
Hmm...

I get that I need to somehow isolate the variables on one side of the equation. I just can't seem to figure out how. It seems like every way I attack it, x and y stay mixed up together.

Are you saying to take

$\displaystyle (-4y)$ and $\displaystyle (1-y^2)$and group them together somehow? - Jul 10th 2007, 03:34 PMJonboy
He's saying identify a b and c.

Remember a quadratic is in the form $\displaystyle (a)x^2\,+\,(b)x\,+\,(c)$ - Jul 10th 2007, 03:44 PMearachefl
That was my first guess as to what he meant, and I did plug those numbers (-1, -4, 1) into the Quadratic Formula, and got the answer $\displaystyle -2 \pm \sqrt 5$. However, this is nowhere near close to the book's answers of

$\displaystyle y = -2x \pm \sqrt{8x^2 +1}$

or

$\displaystyle x = \frac {y \pm \sqrt{2y^2 - 1}}{2}$

so I'm no closer in understanding.

Am I supposed to plug the output of the Quadratic Formula in wherever y appears? - Jul 10th 2007, 10:55 PMJhevon
where did -1, -4, 1 come from?

let's try this hint thing one more time. i will give you a blatant one.

For (a):

$\displaystyle 4x^2 - 4xy + 1 - y^2 = 0$

$\displaystyle \Rightarrow 4x^2 + (-4y)x + \left( 1 - y^2 \right) = 0$

Here, $\displaystyle a = 4 \mbox { , } b = -4y \mbox { , } c = 1 - y^2$

For (b):

$\displaystyle -y^2 + (-4x)y + 4x^2 + 1 = 0$

Here, $\displaystyle a = -1 \mbox { , } b = -4x \mbox { , } c = 4x^2 + 1$

Can you continue now? - Jul 11th 2007, 06:39 AMearachefl
Thanks to all for the hints. My textbook hasn't given any example of this kind of problem, but just dumped the question in our laps regardless.

- Jul 11th 2007, 08:22 PMJhevon