Rational Expressions & Quadratics

[unreal030]

Hey guys I need some help with a problem. I am in a required math business class at college and I and we are doing some review first. Its completely online, I haven't taken any math since Algebra 2 first half of my junior year in High School, so I have forgotten most of it. Seems like most of my class mates are in the same boat since they are of no help.

At any rate, I have gotten through everything except for 2 problems. The book, as usual is of no help so...

If you could explain these two problems to me I would really appreciate it, and I mean every single step, thats usually how the book has been unhelpful. On the offchance it has a similarly formatted problem, the one part where they do something and get this wild number I can't figure out how they went about getting it.

I know these help forums don't usually like "doing" peoples homework. However, this system they use is called MapleTA online, you do the homework, you can do it an unlimited # of times. You don't get a gradesheet (only includes answers, no explanation) once you finalize your HW session. If you want to do it again, it gives you similar problems but all new numbers and maybe slightly differently organized, so this is just so I know how to go through the process when I go through it again.

Thank you in advance.

Rational Exponents and Radicals.

1) Write each expression as a single power of X.

Don't know how to write this on the computer, unlike all of the other stuff but basically its:

x^1/2 over x^1/3 , it is in a single, large parenthesis. Then, in exponent form right outside of the parenthesis is 1/3.

2) Next problem is quadratic formula. I am frustrated with this because I used to be able to do it. I get about halfway through, and I get stuck.

3x^2+2x-4=0

Basically this is what I do:

x=2 plusorminus sqroot 4-4 over 2

since 4-4=0, do I just eliminate that? that only leaves 2+- over 2, what would be my answer??

3) Since that is a little different then some of the other quadratic problems because of the 0, could someone tell me how you get a certain numbers from this example I found in the book??

X^2-2x-1=0

they do:

-(-2) plusorminus sqroot(-2)^2-4(1)(-1) over 2(1)

no problem with that. but then they get this, and don't explain how. basically the sqroot stuff is confusing me. I used to know this but once again, I have forgotten, so the whole (random number)sqroot(random num) confuses me as far as how they got there from the above.

=2 plusorminus sqroot 8 over 2 = 2 plusorminus 2sqroot2 over 2

Thank you again in advance. I appreciate it.

 

[Loren]

x^1/2 over x^1/3 , it is in a single, large parenthesis. Then, in exponent form right outside of the parenthesis is 1/3.

\(\displaystyle (\frac{x^{1/2}}{x^{1/3}})^{1/3}=(x^{1/2-1/3})^{1/3}=(x^{1/6})^{1/3}=x^{1/9}\)

Review the rules of exponents:

\(\displaystyle (a^b)(a^c)=a^{b+c}\)
\(\displaystyle (a^b)^c=a^{bc}\)
\(\displaystyle (\frac{a^b}{a^c}=a^{b-c}\)
etc.

 

[Loren]

\(\displaystyle x^2-2x-1=0\)
Use the quadratic formula...
\(\displaystyle ax^2+bx+c=0\)
\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
In your case a=1, b=-2, c=-1. Plug those into the formula and simplify.

 

[Deleted member 4993]

x^1/2 over x^1/3 , it is in a single, large parenthesis. Then, in exponent form right outside of the parenthesis is 1/3.

\(\displaystyle (\frac{x^{1/2}}{x^{1/3}})^{1/3}=(x^{1/2-1/3})^{1/3}=(x^{1/6})^{1/3}


=x^{1/18}\) ...............small typo

Review the rules of exponents:

\(\displaystyle (a^b)(a^c)=a^{b+c}\)
\(\displaystyle (a^b)^c=a^{bc}\)
\(\displaystyle (\frac{a^b}{a^c}=a^{b-c}\)
etc.

 

[unreal]

bah I turned it in before the typo was noticed

Oh well..the first assignment wasn't many points anyways. Thanks for the help.

 

[Denis]

x^2-2x-1=0
they do:
-(-2) plusorminus sqroot(-2)^2-4(1)(-1) over 2(1)
no problem with that. but then they get this, and don't explain how. basically the sqroot stuff is confusing me. I used to know this but once again, I have forgotten, so the whole (random number)sqroot(random num) confuses me as far as how they got there from the above.
=2 plusorminus sqroot 8 over 2 = 2 plusorminus 2sqroot2 over 2

that's VERY UNCLEAR: -(-2) plusorminus sqroot(-2)^2-4(1)(-1) over 2(1) :
start posting in CLEARER fashion, like:
x = {-(-2) +- sqrt[(-2)^2 - 4(1)(-1)]} / [2(1)]
x = [2 +- sqrt(4 + 4)] / 2

sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2sqrt(2) : kapish?

 

[Deleted member 4993]

bah I turned it in before the typo was noticed

Does that mean you copied the answer WITHOUT THINKING?

You will NEVER LEARN if you continue that way

Oh well..the first assignment wasn't many points anyways. Thanks for the help.

 

[stapel]

bah I turned it in before the typo was noticed

Does that mean you copied the answer WITHOUT THINKING?
You will NEVER LEARN if you continue that way

This points out another reason why it's usually poor practice to provide fully-worked solutions to posters: If all students have to do is copy, then they often don't learn.

What a shame.

If you want to do it again, it gives you similar problems but all new numbers and maybe slightly differently organized, so this is just so I know how to go through the process when I go through it again.

If the system gives different exercises each time, how were you able to turn in the answer you were given?

If you could explain these two problems to me I would really appreciate it, and I mean every single step, thats usually how the book has been unhelpful.

If your book and class aren't teaching the material, then I'm afraid one example, even fully-worked, almost certainly won't give you what you need. And we simply cannot provide the hours of instruction necessary. So please consider using online lessons to obtain the instruction that your school does not provide. (You're not paying for this class, are you?)

. . . . .Google results for "exponents"

. . . . .Google results for "simplifying exponents"

. . . . .Google results for "quadratic formula"

. . . . .Google results for "square roots"

Please give yourself at least a few hours to work through this material!

Eliz.