no, $\displaystyle y = \frac {9 \mp \sqrt {119}~i}{2}$

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- Jul 23rd 2007, 04:37 PMJhevon
- Jul 23rd 2007, 04:38 PMtopsquark
- Jul 23rd 2007, 04:49 PMJhevon
- Jul 23rd 2007, 04:57 PMBlueStar
Okay.

I'll have to be led through on solving this. I cannot brain today, I have the dumb. - Jul 23rd 2007, 05:03 PMtopsquark
The quadratic formula says that

$\displaystyle x^2 = \frac{-9 \pm \sqrt{9^2 - 4 \cdot 1 \cdot 50}}{2 \cdot 1} = \frac{-9 \pm \sqrt{-119}}{2}$

So

$\displaystyle x^2 = \frac{-9 \pm i \sqrt{119}}{2}$

A brief diversion:

$\displaystyle y = -x^2 = - \left ( \frac{-9 \pm i \sqrt{119}}{2} \right ) = \frac{9 \mp i \sqrt{119}}{2}$

Again,

$\displaystyle x^2 = \frac{-9 \pm i \sqrt{119}}{2}$

So

$\displaystyle x =\pm \sqrt{\frac{-9 \pm i \sqrt{119}}{2}}$ <-- The two $\displaystyle \pm$ symbols do not have any relation to each other.

This is technically an unsimplified answer, but in your case I'd leave it like this.

So the solution set is the four points:

The two points

$\displaystyle \left ( \sqrt{\frac{-9 \pm i \sqrt{119}}{2}} , \frac{9 \mp i \sqrt{119}}{2} \right ) $

and the two points

$\displaystyle \left (- \sqrt{\frac{-9 \pm i \sqrt{119}}{2}} , \frac{9 \mp i \sqrt{119}}{2} \right ) $

-Dan - Jul 23rd 2007, 05:09 PMBlueStar
Are those supposed to be the final solutions? Because that seems wrong. It's for a multiple question, and the solution answers only consist of variations of 0 and 5.

- Jul 23rd 2007, 05:12 PMJhevon
- Jul 23rd 2007, 05:23 PMBlueStar
- Jul 23rd 2007, 05:32 PMJhevon
i told you, (0,0) is only a solution if you have a + (y - 5)^2. otherwise, there are NO real solutions. if you did not type the question wrong, topsquark's solutions are correct and the solutions you have are wrong. go back to the question and make sure you have the signs right

- Jul 23rd 2007, 05:41 PMBlueStar
Nope, the signs are right.

- Jul 23rd 2007, 05:54 PMJhevon
- Jul 23rd 2007, 06:12 PMBlueStar
Then either the quiz is wrong or topsquark is, or something weird's going on. :confused:

- Jul 23rd 2007, 06:28 PMJhevon
- Jul 23rd 2007, 08:00 PMBlueStar
Well, I just selected the answer as (0,0) and it was correct.

- Jul 23rd 2007, 08:08 PMJhevon