Math, how i hate it.

[Slochk]

ok guys i need help.
i was given this test and i cant figure it out.

GIVEN:
A+B=1
A^2+B^2=2

A^4+B^4=(X)

(X)=?
(its not 4, 8, 16)

please explain it.
thanks in advance.

[Easton Dark]

Does A^4 mean A > 4 because that would make this a whole lot easier for me to understand it.

[Hon3r]

ooo ooo me! *hand stretched in the air annoyingly*

It's a tough one. If there's an algebraic trick to it, I can't see it.

1) A + B=1
2) A^2 + B^2 = 2

Isolate A in 1) and substitute into 2):
(1 - B)^2 + B^2 = 2
1 -2B + 2B^2 = 2
2B^2 - 2B - 1 = 0

Quadratic formula to find B:

B = [2 +/- SQRT(12)]/4

Simplifies to:

B = 1/2 +/- SQRT(3)/2

Since B has the +/- in it, either is acceptable. That means that if we choose

B = 1/2 + SQRT(3)/2

then A = 1/2 - SQRT(3)/2
(or vice versa)

Square A and B to get
A^2 = 1 - SQRT(3)/2
B^2 = 1 + SQRT(3)/2

Square again to get
A^4 = 1.75 - SQRT(3)
B^4 = 1.75 + SQRT(3)

Adding gives
A^4 + B^4 = 3.5

Geez, what grade is that? That's just tedious.

[Slochk]

thanks guys :D

[killion237]

yeah ^ means what exactly I would like a lesson. :D

[Hon3r]

^ means "raise to the power of"
ex. 3^2 means "three squared" = 9

AHA! I found the algebraic trick.

Square the first equation
A + B = 1
(A + B)^2 = 1^2
A^2 + B^2 + 2AB = 1 <----(expand the binomial square)
2 + 2AB = 1 <----(since A^2 + B^2 = 2)
AB = -1/2 <----(solve for AB)
(AB)^2 = 1/4 <----(square both sides. Call this equation *)

Square the second given equation:
A^2 + B^2 = 2
(A^2 + B^2)^2 = 2^2
A^4 + B^4 + 2(AB)^2 = 4 <----(expand the left side)
A^4 + B^4 + 2(1/4) = 4 <----(using equation *)
A^4 + B^4 + 1/2 = 4 <----(simplify)
A^4 + B^4 = 3.5 <----(solve for A^4 + B^4)

Booyah
Much neater, no need to involve radicals (http://en.wikipedia.org/wiki/Radical_sign), and no using the quadratic formula (http://en.wikipedia.org/wiki/Quadratic_formula#Quadratic_formula).
*is pleased with self*

[Slochk]

You guys rock!

[Easton Dark]

Math is power!

[Slochk]

Geez, what grade is that? That's just tedious.

its my pre-calculus home work. :D, THANK YOU!

[Slochk]

AB = -1/2 <----(solve for AB)
(AB)^2 = 1/4 <----(square both sides. Call this equation *)


can u explain this a bit more?

EDIT: nvm i figured it out lol

EDIT:EDIT:
sry for the double post.

[Deadly]

You aren't allowed to complain until you take AP Physics with a teacher who is an expert in Marine Biology.

To find how much work something does, you take 1/2(mass)(fish)^2 = Joules

[Kenny]

You know, I hate math. However, I actually enjoy programming in several computer languages, it's a little odd.

[nerVe]

I took Algebra, gais...

[Hon3r]

I gave that question to the students in the math club I run. One figured it out in a couple minutes, but most are struggling with it.

Let me know if you have any other questions!
math = awesome

[wertan11]

aww shit. i cant understand that shit at all

[hunterhunter]

......great....now my mind's on that geometry test I have to take tomorrow...

[Slochk]

well my math teacher says it all works out, your the best guys :D