Does the process of mathematics ever lead to more than one correct answer?
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Anonymous2010-12-04 21:51
Definatly use the guadratic formula it can give two answers. In functions in grade 12 you usually use a certain process to find different values for x which can often be more then one or even two.
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Anonymous2010-12-04 22:30
*quadratic
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Anonymous2010-12-05 0:32
>>2
Pretty sure that's not the question, but I could be wrong.
If you're asking, as I interpret it, if you'll ever get two conflicting results, the answer is that that would be the fault of the system and not the process. If you can come up with conflicting theorems, that means your axioms are contradictory.
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Anonymous2010-12-06 1:48
>>4
Actually you can deal with that if you divide the complex plane into True,False,Lie and Error so back to the question of >>1
It is possible if you expand the dimension of the answer.
>>9
Mathfags ITT
The square root of a positive number is always a positive number, however the equation y = x^2 has the two solutions y = +sqrt(x) and y = -sqrt(x)
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Anonymous2011-01-03 2:55
>>12
square root is the same as solving that equation
No, x^n has n answers, for every n-polymonial there are n answers and they're always the only possible ones. If you have some further requirements then you might only include some.
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Anonymous2011-01-08 6:44
>>19
And x2 is designated as the square root, x3 the cube root, etc.
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Anonymous2011-01-08 6:47
>>20
Fucking... I failed this thread by not putting y = xn. I therefore resign all trolling pertaining herein.
>>24
no, youre misunderstanding, roots of a squared number can be negative or positive, but a squared root is always positive
x^2 = 4, so x = -2 or x =2, but root[(-2)^2] and |x| = root(x^2), even though x by itself can be both negative and positive, always returns positive value, as square root returns mod of a number, learn your definitions people
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Anonymous2011-01-10 16:08
>>28
Oh no you dint. Tell me you just dint tell me to learn my definitions..(waves finger above head and does a swivel neck kind of thing)
>>27
"squared" root? OK that's a little silly. No one uses that as a term. I thought you were talking about square roots. Of course if you square a root (or any real), you get positive, assuming the root is real. But square roots just mean solve x^2 = c for x. There are two answers, aka roots. Square roots in this case. That's why we call them square roots in the first place.
>>30
To be honest this discussion is just nonsense. Anyway, squared root means absolute value, and whether you use or not use this term doesnt matter as that's just what it is. Square roots are roots of a 2-polymonial and thats it.
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Anonymous2011-01-14 17:10
Let me clear everything up.
1. There aren't "answers" in math, per se. There are solutions to equations, among other things. When K is a non-negative real number, there are two unique real solutions to (i.e., values of x which satisfy) K = x^2 <==> 0 = x^2 - K. They are x = sqrt(K) and x = -sqrt(K).
sqrt is a function (important! functions can only map values in the domain to exactly one value in the range) defined to be a "canonical" or "principal" square root. It is an arbitrary choice, but was chosen because the positive root is usually more useful.
Hence, it is sensible to say "there is only one square root of K" but "there are two roots to the equation 0 = x^2 - K". Square root is a function, and does not mean "the roots of x^2 = K".
2. There are several places in math where you can arrive at two (or more!) solutions to a problem. Einstein's field equations are a prime example. Depending on the model of the universe you choose, you can have many solutions to the equations! The only rule for anything in math, however, is that the solutions cannot be contradictory, or they cannot lead to a contradiction (e.g., "2 = 1" is a contradiction, and means that either you did something wrong, or your premises were bullshit to begin with).
3. As a follow up to #1, many functions have a so-called "principal branch". Think of a sine wave. Rotate it 90 degrees. You'll see it fails the so-called "vertical line test". So we have to choose a chunk of the function which represents the inverse function. Sometimes this chunk is between (-pi, pi] or [0,2pi). The choice is arbitrary, just like with the square root. With the square root, we choose the [0,inf) chunk as our principal branch.
This junk gets a lot more important when you go full on in complex analysis, where branch cuts are especially important. Ideally all programming languages would state the branch cuts they use for trigonometric functions (some standards do, like Common Lisp and C++). That way it's never ambiguous what something could mean.
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Anonymous2011-01-19 1:01
what country uses term "squared roots" at all? did you make it up>>32
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Xaro2011-01-19 22:34
Yes, a quadratic equation can lead to more than one outcome.
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Anonymous2011-01-20 15:35
>>34
I havent used term "squared roots", I used "squared root" (squaring after taking root) and "square roots" (roots of a 2-polymonial).