anonymous
  • anonymous
I lied, I have one more :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[y ^{4}-3y ^{2}-88=0\]
anonymous
  • anonymous
Again, substitute something for y^2 to get a normal quadratic you can solve
anonymous
  • anonymous
It's just like the others you were doing

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anonymous
  • anonymous
hmm..
anonymous
  • anonymous
Give it a try
anonymous
  • anonymous
i substituted y^4 for y^2 and the y^2 turned into just a y?.. ahh. Idk why this is so difficult for me. I'm sure it's simple.
anonymous
  • anonymous
i meant it the other way around y 2 for the y 4
anonymous
  • anonymous
Use u instead of y for the second variable
anonymous
  • anonymous
it'll be less confusing. Let \(u = y^2\) So \(?\ =y^4\)
anonymous
  • anonymous
u^2?
anonymous
  • anonymous
Yep. So now in your original equation replace all the \(y^2\) with u and all the \(y^4\) with \(u^2\)
anonymous
  • anonymous
the do i want to move everything else to the other side, where it's 0?
anonymous
  • anonymous
No, you need the 0 there in order to use the quadratic equation.
anonymous
  • anonymous
\[au^2 + bu + c = 0\] Means: \[u = \frac{-(b) \pm \sqrt{b^2-4(a)(c)}}{2(a)}\]
anonymous
  • anonymous
Look familiar?
anonymous
  • anonymous
yes it does!
anonymous
  • anonymous
Ok, so plug in your a, b, and c and solve for u, what do you get?
anonymous
  • anonymous
3+/- \[\sqrt{-167}\]
anonymous
  • anonymous
so if it's in the root it would actually be positive. i'm trying to remember.. do I incorporate the 3 with the -167 at all? or did I accurately solve this even?
anonymous
  • anonymous
That's not the right square root
anonymous
  • anonymous
\[\sqrt{(-3)^2 - 4(1)(-88)} = \sqrt{9 +352} = \sqrt{361} \]
anonymous
  • anonymous
So what do you get with that correction?
anonymous
  • anonymous
361
anonymous
  • anonymous
No, I mean for the whole equation.
anonymous
  • anonymous
It came down to 361=19 and those divided =19.. so would it just come to 19 or is there more numbers to that? Everything seemed to cancel out
anonymous
  • anonymous
2a is not 19, it's 2. Look, a= 1, b= -3, c= -88 \[u = \frac{-(-3) \pm \sqrt{(-3)^2-4(1)(-88)}}{2(1)}\] \[ = \frac{3 \pm \sqrt{361}}{2} = \frac{3 \pm 19}{2} \]
anonymous
  • anonymous
So what are the two values we get for u?
anonymous
  • anonymous
11 and -11. 361 squared is 19.. so how are there 4 answers?
anonymous
  • anonymous
Because those are the answers for u. 11, and -8. But \(u = y^2\) So that means y can be?
anonymous
  • anonymous
I already typed the other one in and got it wrong. ha. oops. but thanks
anonymous
  • anonymous
Actually, since u = y^2 u cannot be -8
anonymous
  • anonymous
oh. limited tries?
anonymous
  • anonymous
i have one more problem I have to get right. it's a different problem if you want me to type it on here. otherwise I'll post it to the left
anonymous
  • anonymous
So there's only 2 solutions. u = \(\pm \sqrt{11}\)
anonymous
  • anonymous
yep, thats what it said. thanks!
anonymous
  • anonymous
I have to go to bed I'm afraid. Good luck
anonymous
  • anonymous
THanks for all your help! night

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