anonymous
  • anonymous
Find the values of a so that the equation (a^2-1)x^2+2(a-1)x+1>0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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TuringTest
  • TuringTest
not sure what to do here frankly
anonymous
  • anonymous
Should be finding domain or something.
Zarkon
  • Zarkon
you could complete the square

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More answers

TuringTest
  • TuringTest
agreene and I did that on the other post, but then what do we do with the result?
anonymous
  • anonymous
y=(a^2-1)x^2+2(a-1)x+1 is the original task. Then it says to find the values of a so that the equation would be positive. Answer should be a=(1;infinity)
agreene
  • agreene
\[a\ge 1\] there are a few other--rather odd things you can do the get the rest of the answers.
anonymous
  • anonymous
And how did you get it?
TuringTest
  • TuringTest
yeah I see now agreen showed that this the expression for x in terms of a is not defined for x<1 look at the other post
agreene
  • agreene
the rest of the solutions... are just moving around the answer from the x=(junk) http://www.wolframalpha.com/input/?i=solve+%28a%5E2-1%29x%5E2%2B2%28a-1%29x%2B1%3E0
anonymous
  • anonymous
One possible answer \( -2
TuringTest
  • TuringTest
\[x=\frac{\pm i\sqrt{2}-\sqrt{a-1}}{\sqrt{a-1}(a+1)}\]so this is imagniary when a<1 does that pose a problem though? we already have an imaginary number up top....
anonymous
  • anonymous
I am really not allowed to use imaginary numbers
TuringTest
  • TuringTest
I didn't check agreen's work, so if that i popped up spuriously you have to ask him about it lol
Zarkon
  • Zarkon
\[(a^2-1)x^2+2(a-1)x+1=(a^2-1)\left(x+\frac{1}{a+1}\right)^2+\frac{2}{a+1}\]
agreene
  • agreene
it causes issues for when a<1... in the sense that you end up with answers that are not legitimate--which is why the other answers included x is an element of the reals so, we know to ignore trivial answers. but a >= 1 is a pretty solid answer, the others are very messy and probably extraneous to what ErkoT is doing.
anonymous
  • anonymous
And I get the answer by doing?
TuringTest
  • TuringTest
I'm still trying to figure out where Zarkon is going with his factoring out of a^2-1
Zarkon
  • Zarkon
\[(a^2-1)\left(x+\frac{1}{a+1}\right)^2+\frac{2}{a+1}\] if \(a\ge1\) then the number is clearly positive if \(-1
Zarkon
  • Zarkon
typo if a<-11 choose x=-1/(a+1) then the function overall is negative.
Zarkon
  • Zarkon
geesh...a<-1
Zarkon
  • Zarkon
not sure why your original answer does not include 1
anonymous
  • anonymous
I have absolutely no idea.
TuringTest
  • TuringTest
I'm gonna process that answer while I go enjoy my Sunday playing Skyrim :P
Zarkon
  • Zarkon
\[(1^2-1)x^2+2(1-1)x+1=1>0\]
agreene
  • agreene
I'm gonna play some Starwars the Old Republic to clear my mind i think >.>
Zarkon
  • Zarkon
any MW3 players :)
agreene
  • agreene
I used to play MW3... havent recently though
anonymous
  • anonymous
I just played it an hour ago.
TuringTest
  • TuringTest
not yet still got MW2 and BO everything comes late to Mexico but man, I wanna play you guys!
Zarkon
  • Zarkon
you guys play on steam?
TuringTest
  • TuringTest
steam?
Zarkon
  • Zarkon
I guess not ;)
Zarkon
  • Zarkon
http://store.steampowered.com/
Zarkon
  • Zarkon
I play all of my games through steam
TuringTest
  • TuringTest
Thanks, I'll check it out! PS3 games are so expensive in Mexico, everyone buys pirate Xbox games instead
Zarkon
  • Zarkon
ah...this is a PC/Mac thing
Zarkon
  • Zarkon
I don't play console games...only PC
TuringTest
  • TuringTest
I'll switch to PC games for the next gen probably
agreene
  • agreene
Mexico... I've been there. Me encanta Mérida, Yucatán.
anonymous
  • anonymous
Cool, you guys are from another continent.
agreene
  • agreene
Intercontinental Math Help!
TuringTest
  • TuringTest
nuca he ido alla (no tengo acentos) vivo en Guadalajara visite a Mazamitla y Guanjuato but no, I'm actually american plus, mexico is the smae conctinent ;)
TuringTest
  • TuringTest
nunca
Zarkon
  • Zarkon
ErkoT: where are you
agreene
  • agreene
never went to Guadalajara, meant to... but just didnt.
anonymous
  • anonymous
Europe.
Zarkon
  • Zarkon
I've been to Germany...but that is it
TuringTest
  • TuringTest
I'd like to know the demographics on this site lots of Middle-east as well
agreene
  • agreene
Yeah, lots of Asians--Indian it seems
agreene
  • agreene
I havent made it to Europe yet... probably will after I finish my Masters Degree.
TuringTest
  • TuringTest
me too
Zarkon
  • Zarkon
I was there in 1993 and 1996
TuringTest
  • TuringTest
learn any German? enough to read all those cool German math papers?
Zarkon
  • Zarkon
no
TuringTest
  • TuringTest
lol
agreene
  • agreene
I was 6 and 9 years old, respectively during that time. Ich liebe Deutsch
anonymous
  • anonymous
In 1993 I wasn't even born yet.
agreene
  • agreene
sshh you
TuringTest
  • TuringTest
right!
Zarkon
  • Zarkon
I was in the military...it was for training purposes
TuringTest
  • TuringTest
whoa, didn't expect that o-0
anonymous
  • anonymous
Same.
Zarkon
  • Zarkon
I don't have your typical mathematician background :)
anonymous
  • anonymous
I don't have it either.
TuringTest
  • TuringTest
Nor I You are definitely a mysterious figure Zarkon, and now even more so
Zarkon
  • Zarkon
good...I like it that way ;)
TuringTest
  • TuringTest
figured as much ;)
anonymous
  • anonymous
Alright guys, I'm off. Thank you for your help!

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