Homework: The Other White Meat.

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Postby Game Room Wannabe » Tue Mar 23, 2010 5:54 pm

I hate when people say algebra is easy. Especially more when they try to avoid solving this HARD problem
m+n=3
m²+n²=6
m³+n³=?(27/2)

None of my teachers can solve it... yet people say algebra is easy.



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Postby Wil » Tue Mar 23, 2010 6:03 pm

It is true for (2,1) and (1,2). There is no single solution.

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Postby Rei » Tue Mar 23, 2010 6:23 pm

It is true for (2,1) and (1,2). There is no single solution.
2 and 1 don't work for the second equation.

2^2+1^2=5
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Postby Wil » Tue Mar 23, 2010 6:28 pm

That's why you use 1 and 2, not 2 and 1... duh!

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Postby CezeN » Tue Mar 23, 2010 6:36 pm

I think the answer is no solution, but what do I know *shrug*
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Postby neo-dragon » Tue Mar 23, 2010 6:41 pm

If I'm not mistaken,

n = 2.366025404
m = 0.633974595

or to be more exact,

n = (6 + 12^0.5)/4

m = 3 - [(6 + 12^0.5)/4]

I find it hard to believe that your math teacher couldn't solve that.


*corrected the -4 error.
Last edited by neo-dragon on Tue Mar 23, 2010 7:55 pm, edited 1 time in total.
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Postby CezeN » Tue Mar 23, 2010 6:58 pm

I know my Algebra 2 teacher, last year, wouldn't have been able to solve it, either.
She didn't really teach that well, and when I asked her one question off my SAT practice book, which was hard, she wasn't able to answer.

Neodragon, how exactly did you figure it out?
What steps?
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Postby neo-dragon » Tue Mar 23, 2010 7:05 pm

- rearrange the first equation to isolate one variable.
- substitute into the second equation so that it now has only one variable.
- expand and collect like-terms, and bring everything to one side of the equation so that it is in the form ax^2 + bx + c = 0
- Use the quadratic equation, which will give two possible solutions, only one of which works with the third equation.

Not to sound smug or anything, but any high school level math teacher should be able to solve that pretty easily since the only trick is using the quadratic equation which is taught in what, 9th grade?
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Postby Wil » Tue Mar 23, 2010 7:05 pm

n = 2.366025404
m = 0.633974595
... I was rounding. :D

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Postby Game Room Wannabe » Tue Mar 23, 2010 7:05 pm

m+n=3 (m+n)(m+n) = 9 = m²+2mn+n²
m²+n²=6 so 2mn=3 mn=3/2
(m+n)(m²+n²)=m³+m²n+mn²+n³=18
mn(m+n)=m²n+mn²=9/2
so m³+n³=27/2

2 SOLUTIONS

m=(3+sqrt3)/2
n=(3-sqrt3)/2

n=(3+sqrt3)/2
m=(3-sqrt3)/2

m²+n² = [(3-sqrt3)(3-sqrt3)]*[(3+sqrt3)(3+sqrt3)] (make it simpler, 1/2 x 1/2 = 1/4) = [9-2sqrt3+3]+[9+2sqrt3+3] / 4 = 24/4=6



Any more questions? I'm only in Geometry... Freshman in hs...

Things that I hate: problems like the above
If I'm not mistaken,

n = 2.366025404
m = 0.633974595

or to be more exact,

n = (6 + 12^0.5)/-4

m = 3 - [(6 + 12^0.5)/-4]

I find it hard to believe that your math teacher couldn't solve that.
Not in simplest form. n=(-3/2 - sqrt 3) is incorrect.
m=3 - [-3/2 - sqrt 3/2] is also incorrect.
n=(6+12^0.5)/4 is correct.
m=3-[(6+12^0.5)/4] is also correct.

Don't you just hate those?
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Postby neo-dragon » Tue Mar 23, 2010 7:23 pm


m=(3+sqrt3)/2
n=(3-sqrt3)/2

n=(3+sqrt3)/2
m=(3-sqrt3)/2
Yes, I just didn't take the time to simplify my solution.
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Postby Game Room Wannabe » Tue Mar 23, 2010 7:26 pm


m=(3+sqrt3)/2
n=(3-sqrt3)/2

n=(3+sqrt3)/2
m=(3-sqrt3)/2
Yes, I just didn't take the time to simplify my solution.
Both solutions on the bottom were wrong, simplified or not. Again, it is /4 not /-4
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Postby neo-dragon » Tue Mar 23, 2010 7:35 pm

You're right. I threw in an extra negative in the rational form by accident, but my math is still right. :wink:

btw, have you learned the quadratic equation?
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Postby Game Room Wannabe » Tue Mar 23, 2010 7:41 pm

You're right. I threw in an extra negative in the rational form by accident, but my math is still right. :wink:

btw, have you learned the quadratic equation?
I have, I don't see how you could possibly use it in there effectively. Isn't my way more clearcut? I mean, who wants to round during a test when you can "not round" and go exact?
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Postby neo-dragon » Tue Mar 23, 2010 7:44 pm

You find what you did to be simpler? I don't, but do what works for you. And you don't have to round, just simplify and you get the same thing.

I explained step-by-step how to use it effectively.
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Postby Game Room Wannabe » Tue Mar 23, 2010 7:59 pm

You find what you did to be simpler? I don't, but do what works for you. And you don't have to round, just simplify and you get the same thing.

I explained step-by-step how to use it effectively.
Boo, show work with it.

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EDIT: sqrt for roots, ± for pos/neg,
²
³
and that's really everything you need.
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Postby Sonikku13 » Tue Mar 23, 2010 8:00 pm

You find what you did to be simpler? I don't, but do what works for you. And you don't have to round, just simplify and you get the same thing.

I explained step-by-step how to use it effectively.
Boo, show work with it.

I HATE ROCK AND ROLL!!
TAKE A DIME OUT OF THE JUKEBOX BABY!!
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lol

EDIT: sqrt for roots, ± for pos/neg,
²
³
and that's really everything you need.
You do know that neo-dragon is a teacher, right?
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Postby Game Room Wannabe » Tue Mar 23, 2010 8:01 pm

You find what you did to be simpler? I don't, but do what works for you. And you don't have to round, just simplify and you get the same thing.

I explained step-by-step how to use it effectively.
Boo, show work with it.

I HATE ROCK AND ROLL!!
TAKE A DIME OUT OF THE JUKEBOX BABY!!
I HATE ROCK AND ROLL!!
lol

EDIT: sqrt for roots, ± for pos/neg,
²
³
and that's really everything you need.
You do know that neo-dragon is a teacher, right?
Uh, no, and yeah, teach me then. I showed work with mine :roll:
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Postby neo-dragon » Tue Mar 23, 2010 8:06 pm

I think I've been generous enough :) .
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Postby human. » Tue Mar 23, 2010 8:07 pm

Now, give us a lecture on redox equations! Please?? They're some of my favorite. =]

btw, I hate physics C.

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Postby Sonikku13 » Tue Mar 23, 2010 8:08 pm

I need to learn calculus operators.
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Postby Game Room Wannabe » Tue Mar 23, 2010 8:16 pm

- rearrange the first equation to isolate one variable.
- substitute into the second equation so that it now has only one variable.
- expand and collect like-terms, and bring everything to one side of the equation so that it is in the form ax^2 + bx + c = 0
- Use the quadratic equation, which will give two possible solutions, only one of which works with the third equation.


Oh come on, and in a test situation I'm supposed to remember this?

hmm m+n=3
m=n+3
m²+n²=(n+3)(n+3)+n²
Loads of work to me... I think it's wrong at this stage...
6=2n²+6n+9
0=2n²+6n+3
Oh come on, guessing during a test? HATE IT...
n=(-6 ± sqrt[36-4(3)(2)])/4
n=(-6 ± sqrt[12])/4
n=-3/2 ± sqrt 3/4

Oh what now, roots in here too?
You don't have to solve for a variable, you know.
3+ 3/2 - sqrt 3/4 = m
-3/2 + sqrt 3/4 = n

now for (9/2 - sqrt 3/4)^3 + (-3/2 +sqrt 3/4)^3

I ain't even gonna do that...
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Postby Gravity Defier » Tue Mar 23, 2010 8:22 pm

hmm m+n=3
m=n+3
You didn't last long...you can't just pick up and move the variable. You're subtracting it from both sides, in essence, so that should be m= -n + 3.


But I quit teaching this subject for a reason...

Oh, wait. Hah.
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Postby Caspian » Tue Mar 23, 2010 8:24 pm


hmm m+n=3
m=n+3
Here's your first mistake.

If m+n=3 then
m=(-n)+3
or
m=3-n
It's not "noob" to rhyme with "boob". It's "newbie" to rhyme with "boobie".

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Postby Sonikku13 » Tue Mar 23, 2010 8:26 pm

Everyone makes silly mistakes once in a while, right?
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Postby Game Room Wannabe » Tue Mar 23, 2010 8:35 pm

I'm a state champion dangit... going on me for 1 mistake lol

But yeah, it gets complex is the idea. Would you rather have algebra that stays relatively simple :roll: , or LOADS AND LOADS OF FRACTIONS? :twisted:
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Postby zeroguy » Tue Mar 23, 2010 11:00 pm

I hate when people say algebra is easy.
'algebra' is easy. The trick is, when you get to a problem that uses
the quadratic equation
to solve, you always skip it if possible. I remember solving many problems to that point, and then saying "ugh, I don't want to reduce that", and going to the next problem.

The only time that definitely doesn't work is the homework for the math lesson where you learn the quadratic equation, since all of the questions tend to involve it. Most other times, only one problem in so many use it, so I figured I can just take the hit.

Also, it just seems easier in comparison to some other things you may learn. Like surface integrals! Jacobians! Man, I have no idea how to do that stuff anymore, it's amazing. Or just plain trig. Boo, trig.
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Postby locke » Wed Mar 24, 2010 3:48 am

- rearrange the first equation to isolate one variable.
- substitute into the second equation so that it now has only one variable.
- expand and collect like-terms, and bring everything to one side of the equation so that it is in the form ax^2 + bx + c = 0
- Use the quadratic equation, which will give two possible solutions, only one of which works with the third equation.


Oh come on, and in a test situation I'm supposed to remember this?
Dude I haven't had a math class in... nearly eight years... and that's how I started to solve it before I said, "why? I haven't had a math class in nearly eight years... I wonder if Neo or Alea posted, that will save me time."
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Postby Game Room Wannabe » Wed Mar 24, 2010 6:09 pm

I hate when people say algebra is easy.
'algebra' is easy. The trick is, when you get to a problem that uses
the quadratic equation
to solve, you always skip it if possible. I remember solving many problems to that point, and then saying "ugh, I don't want to reduce that", and going to the next problem.

The only time that definitely doesn't work is the homework for the math lesson where you learn the quadratic equation, since all of the questions tend to involve it. Most other times, only one problem in so many use it, so I figured I can just take the hit.

Also, it just seems easier in comparison to some other things you may learn. Like surface integrals! Jacobians! Man, I have no idea how to do that stuff anymore, it's amazing. Or just plain trig. Boo, trig.
I actually prefer the formula...
"Find the area of a square with diagonals 1 inch longer than its sides."

oh yay, more quadratics...

x sqrt 2 - x = 1
x(sqrt 2 - 1) = 1
x^2(2-1)=1
x^2=1
^WRONG!!

x sqrt 2 ^2 = 2x^2
2x^2=(x+1)(x+1)
2x^2=x^2+2x+1
-x^2+2x+1=0

yuck, I ain't gonna factor that... you can't.

x = [-2 ± sqrt( 4 + 4 )] /-2
x = [-2 ± 2 sqrt 2] /-2
x = 1 ± sqrt 2

A= X^2

(1 + sqrt 2)^2=
1 + 2 sqrt 2 + 2 =
3 sqrt 2 = A

and yeah, would you want the formula, or to factor -x²+2x+1=0?
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Postby Sonikku13 » Wed Mar 24, 2010 6:31 pm

-x^2+2x+1=0
x^2-2x-1=0
x^2-2x=1
x^2-2x+1=2
(x-1)^2=2
x-1=-sqrt 2 or x-1=sqrt 2
x=1-sqrt 2 or x=1+sqrt 2

Completing the square is easier than the quadratic formula. I don't like it when I have to show the quadratic formula when it is much easier to complete the square.
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Postby Game Room Wannabe » Wed Mar 24, 2010 6:45 pm

-x^2+2x+1=0
x^2-2x-1=0
x^2-2x=1
x^2-2x+1=2
(x-1)^2=2
x-1=-sqrt 2 or x-1=sqrt 2
x=1-sqrt 2 or x=1+sqrt 2

Completing the square is easier than the quadratic formula. I don't like it when I have to show the quadratic formula when it is much easier to complete the square.
... Why did I forget this?

m+n=3
m=-n+3
m^2+n^2=6
m^2=-n^2+6
mn=3/2

m=(3 - sqrt 3)/2 n=(3 + sqrt 3)/2
so, you arose from 3 ± sqrt 3 /2
6 ± sqrt 6/4
or just the simple way
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27 rooted = 3×3×3
so, 3, 3
3 , sqrt 3
sqrt 3 / sqrt 27 = 3
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Postby Jayelle » Wed Mar 24, 2010 9:08 pm

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Postby Syphon the Sun » Thu Mar 25, 2010 8:48 am

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Postby Young Val » Thu Mar 25, 2010 9:18 am

WIN.
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I'm pushing through
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and I can
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Postby Luet » Thu Mar 25, 2010 10:05 am

I still remember the quadratic equation even tho I've been out of high school for 15 years. Then again, I love math. I also love trig...and logarithms. Do they still teach logs?
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