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Algebra geniuses out there?
Old 07-12-2009, 10:07 PM   #1
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Algebra geniuses out there?

Any of you late hour keepers want to show off your skills?
I have one problem on my homework that I think I don't have right--the answer needs to be a simplified fraction and radicals, and can't be in decimal form.

x squared plus 5/2 x = 5

The two answers I got for x are
1/4 (-5 - square root 105) , 1/4 (square root 105-5)

Only one more week of algebra to go!
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Old 07-12-2009, 10:42 PM   #2
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I agree, but to remove any possible ambiguity, I'd rewrite the second answer to be more like the first: 1/4(-5 + sqrt 105)

the way, you wrote it, a possible (mis)interpretation would be 1/4(sqrt(105-5)) although
you didn't write it that way
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Old 07-12-2009, 10:44 PM   #3
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Sarah, what I did was first subtract 5 from both sides, and then multiply each term by 2, to get

2(x squared) + 5x - 10 = 0 as our equation to solve.

Then, the answer I got was
(-5 + (square root of 105))/4
(-5 - (square root of 105))/4

It's been years! Hope I did it right. Whew! Looks to me like you got it right.
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Old 07-12-2009, 10:49 PM   #4
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I think that is the right form, once I looked at it. One of the things that confuses me so much is doing approximate versus exact and do simplified fractions mean you leave it over the 2, etc.
Thank you very much, both of you! I don't know how people remember this stuff--it has been 20 years since I last had algebra, and I haven't kept a single bit of it. Argh!
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Old 07-12-2009, 11:04 PM   #5
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-b +/- sqrt ( b*b -4ac ) / 2a

x*x + 5/2 x = 5

1*x*x + (5/2)x -5 = 0

so a=1, b=5/2, c= -5

-b +/- sqrt ( b*b -4ac ) / 2a

-(5/2) +/- sqrt ( 25/4 +20) / 2

-(5/2) +/- sqrt ( 105/4 ) / 2

-(5/2) +/- sqrt(105) /2 / 2

-5 +/- sqrt(105) / 4

Also, the online decimal calculators agree with this answer (same as you have)
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Old 07-12-2009, 11:05 PM   #6
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Thanks, y'all! I submitted my homework (that was the last question I was having trouble with) and made an 83%! Got that one right, thanks to my smart peeps.
I'll hunt all of you down next week when I'm choking on the final.
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Old 07-13-2009, 08:08 AM   #7
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growingolder:
Hard to write a math looking formula on the computer, but you did a good job. I believe this is the formula for solving a ploynomial equation: x equals minus b plus or minus the square root of b squared minus 4 times a times c divided by 2 times a. Doesn't even sound right putting it into words but that's it.
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Old 07-13-2009, 12:20 PM   #8
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Are you allowed to use the quadratic formula or do you actually have to show all the work by completing the square?
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Old 07-13-2009, 12:38 PM   #9
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Are you allowed to use the quadratic formula or do you actually have to show all the work by completing the square?
My opinion is that it is much more meaningful to do the latter........50 yrs
from now, I doubt that you'll remember the formula. I couldn't even remember where the a,b,c went as coefficients. .......but if do the completing the square method, you'll understand the principle and have at least a fighting chance of doing it from scratch even when you're gray-haired in your rocking chair. An interesting exercise along the same line is to derive the quadratic formula from scratch.

The way OP posted the problem, it almost looked like they wanted you to
complete the square.
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Old 07-13-2009, 12:43 PM   #10
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Are you allowed to use the quadratic formula or do you actually have to show all the work by completing the square?
You so nicely corrected my wording ziggy, it is a quadratic equation. Haven't touched that kind of stuff since 1957. See how much you can forget?
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Old 07-14-2009, 03:18 PM   #11
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Okay, here's another one for you:

Simplify the 16th root of (-10) ^ 16

That is the 16th root of negative ten raised to the 16th power.

I think it is 10, but I'm wondering if -10 is right.

One more:

cube root of 20 .
I have to rewrite with a rational exponent. I can't use decimals, only fractions.

I've got 2 * cube root of 2 1 / 2

I have been using the quadratic formula and the long division method in this class, but we also learned completing the square and factoring. Depending on the equation, we had to show work for each of them.

The two problems above, I don't have to show work.
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Old 07-14-2009, 03:51 PM   #12
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Originally Posted by Sarah in SC View Post
Okay, here's another one for you:

Simplify the 16th root of (-10) ^ 16

That is the 16th root of negative ten raised to the 16th power.

I think it is 10, but I'm wondering if -10 is right.
In the real numbers, (-x)^2n = x^2n for all integers n. Therefore this number is the same as 10^16, and the 16th root is simply 10. Furthermore, any "even root" (square root, 4th root, (2n)th root) of a real number is positive. Which makes sense, because when you repeatedly multiply a negative number by itself the results are positive, negative, positive, negative....

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Originally Posted by Sarah in SC View Post
One more:

cube root of 20.
I have to rewrite with a rational exponent. I can't use decimals, only fractions.

I've got 2 * cube root of 2 1/ 2
The cube root of x is simply x to the 1/3 power.

So therefore, the cube root of 20 is just 20^(1/3).
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Old 07-14-2009, 04:13 PM   #13
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Quote:
Originally Posted by Sarah in SC View Post
Okay, here's another one for you:

Simplify the 16th root of (-10) ^ 16

That is the 16th root of negative ten raised to the 16th power.

I think it is 10 , but I'm wondering if -10 is right.
A similar example is this:

Qn: If x^2 = 4, what is x?
Ans: x = +2 or -2

Addendum question:

If x^2 = -4, what is x?
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Old 07-14-2009, 04:17 PM   #14
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A similar example is this:

Qn: If x^2 = 4, what is x?
Ans: x = +2 or -2
It can be both, but I guess I'd check to see how the material was being covered in class. Sometimes they are implicitly seeking only the "positive" square root. So depending on what was being taught and how, the answer could either be 10 or +/-10.
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Old 07-14-2009, 04:21 PM   #15
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I'm going to have nightmares of my Algebra classes now....
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Old 07-14-2009, 04:57 PM   #16
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Me, too, Bam!

I am soooo impressed by the help you're getting, Sarah! When they told me I would never need to know algebra in the real world I believed them, so I got nothing.
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Old 07-14-2009, 06:06 PM   #17
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Originally Posted by indexfundfan View Post
Addendum question:
If x^2 = -4, what is x?
x = 2i where i = sqrt(-1) 1 = 1 angle 0, -1 = 1 angle 180
i = 1 angle 90

1 (or +1) can be thought of as a horizontal line from 0 to +1
-1 can be thought of as a hor. line from 0 to -1 or the +1 line rotated 180 deg or 2 90 deg rotations
1i can be thought of a vertical line from 0 to + 1 or a 90 deg rotation
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Old 07-14-2009, 06:20 PM   #18
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Boy that sure makes sense the way you explain it.
Okay, thanks y'all, very much!
I have a logical mind, but believed it when they told me I was bad at math.
Those very logical explanations really help.
I guess I keep thinking there is a "trick" somewhere that I missed.

BBB and Feever, you know I'm right there with ya!
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Old 07-14-2009, 06:38 PM   #19
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I prefer Algebra-less...
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Old 07-14-2009, 07:20 PM   #20
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HFWR, for you we will have a special "bra-burning math" book written

ta,
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