# Thread: Trouble with a simultaneous equation

1. ## Trouble with a simultaneous equation

I'm having trouble with this. I could swear everything is done right, but then I get to the end and substitute in the values to the original formulas and they don't come out correctly.

2. Originally Posted by Naur
I'm having trouble with this. I could swear everything is done right, but then I get to the end and substitute in the values to the original formulas and they don't come out correctly.
haha, what you wrote is kind of confusing.

$5 = p(q - 1)$ ...............(1)
$12.5 = p(q^2 - 1)$ ..........(2)

if so, what you did is overkill. note that $q^2 - 1$ is the difference of two squares. so,

$12.5 = p(q - 1)(q + 1)$

wait! what's this?!

$12.5 = {\color{red}p(q - 1)}(q + 1)$

now where have i seen that before?

3. Holy tits, you're a genius.
Sorry, yes, they're my two equations.
p(q-1) turns out to be equation 1, which equals 5, so q = (12.5/5)-1, etc, and you're correct!

But, if you don't mind, I'd still like to know what I did wrong originally.

4. Originally Posted by Naur
Holy tits, you're a genius.
Sorry, yes, they're my two equations.
p(q-1) turns out to be equation 1, which equals 5, so q = (12.5/5)-1, etc, and you're correct!

But, if you don't mind, I'd still like to know what I did wrong originally.
you made a classic mistake. but of course, it drives math nuts...well, nuts.

you pulled a $(x + y)^2 = x^2 + y^2$ thing. that is WRONG! and yes, infuriating

$(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2$

where did you do this? you wrote $\bigg(\frac 5p + 1 \bigg)^2 = \frac {25}{p^2} + 1$. that is wrong

$\bigg( \frac 5p + 1 \bigg)^2 = \frac {25}{p^2} + \frac {10}p + 1$

5. Oh yes, that one. I learnt not to make that mistake only a little while ago, but then the fraction threw me off.
Thanks very much. I'll watch out for that one in the future...hopefully.

6. Originally Posted by Naur
Oh yes, that one. I learnt not to make that mistake only a little while ago, but then the fraction threw me off.
Thanks very much. I'll watch out for that one in the future...hopefully.
yes, watch out for it. to help you remember, just know that you will be hurting Jhevon if you make that mistake again

7. Oh god no, I'll pay extra attention to it.