1. ## Summer School

Okay, So I'm in an accelerated Algebra II course for this summer and things just seem to be moving so fast, at first nothing made sense, now I'm beginning to understand certain things but even after reading through purple math and several other sites, I still can't make sense of certain problems. We have a test everyday and since I didn't understand anything the first few days (last week was the first week) My average is now a 68 . However On Friday last week I think I did a little better on the test and today I felt confident as well, but knowing myself I still probably only scored in the 80s.

Now that I'm done ranting...

I'm probable going to post questions in this thread everyday if you don't mind giving me advice I would GREATLY appreciate it.

So for starters, what to do with expressions like this:

3*√x^10 (in case my notation is bad: the cubed root of x to the tenth power)

Next:
Tonight my HW included (and the test tommorrow will include):
-Extracting square roots:
x^2 - 6x +2 =0

I understand how to get to here:
x^2 -6x +9 = 7

but do not understand getting here:
(x-3)^2 = 7

from this step on however I can solve these.

-Complex numbers:
-adding and subtracting is simple enough, just treat "i" like a variable
-Multiplication also doesn't seem that scary if I just remember to take any "i" to the power of 2 and change it to a negative one(i^2=-1).
-division isn't so bad either, just multiply the by the conjugate base.

the problem is with things like this:

3i * (4+5i)^2 = 3i(16+10i+25i^2) =48i+30i^2+75i^3
(4-5i)^2 (4+5i)^2 (1?)

where do I go from here? what exactly happens to the denominator? will it always cancel completely (did it even do that here?)?

And Lastly...
Polynomial equations
???????????
that means like any type of polynomial, solving for x! Some of them I can do, but there are so many different types!

First of all I have no clue what to do when you have a fractional exponent:
4x^3/2 - 8 = 0

the book adds 8 then divides by 4, I'm good up to here:

x^3/2= 2

But what did they do to get the 3/2 onto the two like this:

x=2^2/3

Next up are equations with radicals:
I guess I'm really okay with these, it's just sometimes they pop up in equations and I get confused, I'll list a bunch of equations that confuse me at the end of this (long) post.

WORD PROBLEMS:
A college charters a bus for $1700. 6 more students join and the cost per student drops$7.50. How many students were in original group.
►how to set up and explanation, please!

Complex interest:
deposit of2500, matures to 3052.49 after five years. interest is compounded monthly. how to solve for interest, since its part fraction which is part of a quantity being squared, I get confused.

These are all the types of problems, but there are some specific ones which I can't seem to solve:

36) (3+√-5)(7-√10)

16) 36t^4 + 29t^2-7 =0

36) x + (√31-9x) =5

44) 4√x-3 - √6x-17 =3

52) 4x^2(x-1)^1/3 + 6x(x-1)^4/3

2. Originally Posted by keybowvio
...

So for starters, what to do with expressions like this:

3*√x^10 (in case my notation is bad: the cubed root of x to the tenth power)
You can change this term into: $\displaystyle \sqrt[3]{x^{10}} = \left(x^{10} \right)^{\frac13} = x^{\frac{10}3}$

Next:
...
I understand how to get to here:
x^2 -6x +9 = 7

but do not understand getting here:
(x-3)^2 = 7

from this step on however I can solve these.
You are supposed to know
$\displaystyle (a+b)^2 = a^2+2ab+b^2$ ....... and

$\displaystyle (a-b)^2 = a^2-2ab+b^2$

That means if you have a sum like the RHS of the formulae which represent a complete square you can write it as a square.

the problem is with things like this:

3i * (4+5i)^2 = 3i(16+10i+25i^2) =48i+30i^2+75i^3
(4-5i)^2 (4+5i)^2 (1?)

where do I go from here? what exactly happens to the denominator? will it always cancel completely (did it even do that here?)?
Unfortunately the problem is nearly unreadable ...

Maybe you are asked to simplify

$\displaystyle \frac{3i}{4-5i} = \frac{3i}{4-5i} \cdot \frac{4+5i}{4+5i} = \frac{12i+15i^2}{16-25i^2}=\frac{12i-15}{41}$

And Lastly...
Polynomial equations
...
First of all I have no clue what to do when you have a fractional exponent:
4x^3/2 - 8 = 0

the book adds 8 then divides by 4, I'm good up to here:

x^3/2= 2

But what did they do to get the 3/2 onto the two like this:

x=2^2/3
You have to transform the equation until you have only the unknown to the power of something. Then you want to get the unknown to the power of one. Use the property:

$\displaystyle \left(x^a\right)^{\frac1a} = x^{\frac aa} = x^1 = x$

$\displaystyle \left(x^{\frac32}\right)^{\frac23}= 2^{\frac23}$
$\displaystyle x^1 = \sqrt[3]{4}$