Attention Math People: Help Needed!

[Marzipan]

I'm having trouble with a problem that the student I'm tutoring got for homework. It's solving for X, where X is the short side of a triangle.

The original problem is that a right triangle has the following sides:

A=X
B=X^2-5
C=2X^2-13

After FOIL-ing for the Pythagorean Theorem, I've gotten to 3x^4+43x^2-144=0 and there am I stuck. The only thing I can think of is that he copied down a sign incorrectly from the board and it should be 3x^4-43x^2+144=0. Can anyone help me here?


He also had a problem where he had to find the x-intercepts for
f(x)=X^4-2x^2-15

One of our answers was "sqrt -5" which isn't an x-intercept because it is imaginary, but his teacher indicated it should be included anyway. I don't think much of her, actually.

[Brooke]

I'm not even going to look at it right now. LOL Anika (MathSpeak) is a math genius though. I'd try PMing her and asking her to take a look. This is the kind of thing she loves, I bet. :D

[Lori]

:yup Anika is your girl for this one. ;)

[Kristen]

I was coming to say the same thing. :giggle

[MathSpeak]

I sent you a PM ;)
This is where you ran into trouble: 3x^4+43x^2-144=0
the sign on the x^2 is switched... should be -43

I also suggested you replace all of your x^2s with y...
so you'll have 3y^2-43y-144=0... which is a heckuva lot easier to solve for.
JUST REMEMBER that when you plug in your values, you have to take y^.5 to get your x

I think that covers it all...

Off to look at problem #2 for you...
OH, do you want me to post the answers I got? Just so you can make sure?

x=3
and that gives you a right triangle with sides = 3,4,5
and then x=1/3 (which works as far as the quad equation goes, but gives you a negative length for your hypotenuse... and, obviously, won't work...)
You're gonna wanna go with x=3

Let me know if you have questions. I PMd you my cell phone number!

[MathSpeak]

Oh, I should mention that I think he copied the problem right, but when it was FOILed out, the sign was transposed... make sense? I just copied the original problem and worked it on paper from scratch... and I got the -43

[MathSpeak]

For your intercept problem, the roots are sqrt 5 and sqrt -3

So, you would say the intercepts occur at sqrt 5 and sqrt 3* i

with i being sqrt (-1)

[Marzipan]

Thanks Anika. I see where the sign was transposed. For the second problem, sqrt3 doesn't solve the original equation, but sqrt5 does. And since it is an intercept problem (the question related to the motion of a proton) I don't see how he can submit i-sqrt3 as an answer, as it is an imaginary number and cannot be plotted.

ETA: If you don't mind, I'd still totally appreciate the fax. Figures it would be a 3-4-5 triangle. Classic!

[MathSpeak]

I am SOOOO sorry... I can definitely send you the fax in about 10 mins. It's Month end at my acctg job and I'm still kinda in training, so I didn't know I was going to get snatched away from my desk. LOL. I'll send it (hope you can read my handwriting :))
For the second prob, it's sqrt -3 (negative 3), so if you plug in sqrt3 TIMES i, then it works. The reason you have that imaginary intercept is that you're working in the 4th order... it's not uncommon. Conceptually, it doesn't make sense... LOL

[Shana]

Anika, you are so so so AMAZING sister!!!!

[Amy J]

it all looks like a bunch of symbols and numbers to me! Did I mention I pass college math with a very high grade of D. I can't understand math to save my life.

[SabrinaJL]

:eek Anika, if I've never told you how awesome I think you are, let me tell you now. Where's that little bowing smilie when you need it? LOL

[Mary]

OMG, I started trying to read this and my brain just completely shut down. LOL I'm going to have to go read a book for a little while to get it moving again. Anika, you are amazing. :)

[MathSpeak]

You ladies are entirely too sweet :) Thank you.
When Brooke wrote "This is the kind of thing she loves I bet"... I couldn't help but smile. You all know me well :rofl

[Marzipan]

Anika, thanks again. I'm mortified to have even had trouble with that first problem. straightforward as it is. I can't believe I made such a dumb mistake with that sign in front of the 43! I'm going to chalk it up to having had a nasty cold all week. ;)

As for the second, my only annoyance is with his teacher. The problem isn't difficult in any way, but her phrasing of the question was silly.

[MathSpeak]

Oh, not a problem at all... did you see my chicken scratch fax? LOL You provided me a MUCH NEEDED break. I enjoy Math a whole lot more than pure accounting! I hope you feel better soon!

[Kristen]

Anika, you are amazing! I'm sure I could figure the problem out, given enough time and enough instruction books, but I am amazed by your passion for it! I've always done fine in math, but it has never inspired or excited me. I get more thrilled over spelling and vocabulary. :giggle

[yummymommy]

wow Anika you are awesome! That looked like chinese to me or something, I couldnt get that if my life depended on it!!! :giggle

[Brooke]

And now, I want to see if I can get it before reading the hints/answers. LOL I've stayed away all day yesterday and today until I had time to play with it.

[Brooke]

Ok,never mind. I do not remember enough geometry and algebra, apparently. That's so sad, I used to love to do proofs. :bagover:

[MathSpeak]

:rofl I LOVE the smilie!!!!!

[Jo]

I just wanted to let everyone know that I left this for someone else to answer because I wanted to see if anyone was as smart as me......NOT!:hehe

WTG Anika! I have no idea that the problem was even about.LOL