Does -3^2 = 9 or -9? Discuss.
I will never know.
Ask a precise question and you’ll get an precise answer.
Depends if it is -1*(3²) or (-3)², which could be defined with parenthesis.
We also don’t know if it’s the result of a rewritten equation already or the basis offered, nor the context to make a clear statement.
You tell me where it comes from and which one it is, and depending on that it’s either one.
Might as well come from (4-5)*(1+2)² with some shaky math. Common mistake to end up with -3²
IMO in this case it’s obvious though, even if you pull the -1 out. You got to put it in parenthesis if you do so, so you’ll end up with (-1*3)² which is 9, just like -3².
But there are equations where it’s not that obvious and parenthesis save lives… literally (engineering for instance)
Is that OK, or is this a mathtrollthread again? Then I could come up with some stuff to advocate -9 people would buy
Haha, I agree, with you the answer is 9, but many will argue that -3^2 is by “standard” considered -(3)^2 which is ridiculous, but hey what can I do about it.
Wouldn’t (4-5)(-(1+2))^2 more accurately represent this equation hmm? Let the trolling begin! lol
I don’t really see the point with starting a new thread for this, but here is what I wrote in your previous thread anyway.
Having to add brackets around a single number to make it behave as a single number just seems completely wrong to me.
Take for example the expression -2x^2, the ^2 only applies to x, so I don’t really see why it should make a difference if the number before x is 1 or 2
Yes but the 2 is not a 1, and it will change the value of x^2 when it is discovered, it does not get its value from x, -x^2 on the other hand does have a -1 in front of it, but 1 is unique in that it will not change the final result, therefore it will follow x in the exponent operation, 1’s follow every number into there respective operation, as every number can be multiplied by 1 without changing the value. the positive or negative symbol in front of the 1 dictates the values of the number that immediately follows, thinking about this only makes math feel more complicated and it can be ignored, in its place you can have the positive or negative symbol follow the value that immediately proceeded it, in all the operations that are carried out on that value, by value I am actually referring to the full value, this means that -2(1+2+3) is actually -12(11+12+13) and that 23 - 105 is actually
1((12)(13)) + 1(-110)(15)) which is:
1(1(12)1(13)) + 1(-1(110)1(15)) etc…
This is use full knowledge though, as it allows you to understand why you can move values around within an equation, such as:
12-63 = -63+12
Ok, so are you saying that -x^2 = x^2?
no, I am saying that -x^2 = -x*-x
I did make a small error in the math on my post, if you would be so kind as to update your comment plz lol
wow homework help. why am i not surprised. LOL
well, -x*-x = (-x)^2 = (-1)^2*x^2 = x^2
if you answer -3^2 with -9 then you have performed this operation: -133, which should be clear in the original equation, represented as -(3)^2, if you answer -3^2 with 9 then the operation you have performed is -3*-3, which should be represented as:
-3^2 or (-3)^2.
so -x*-x = (-x)^2 = (-1x)(-1x) = -x^2
I guess we’ll just have to agree to disagree on this one.
I just don’t think that you should write -3^2 if you want the ^2 to apply to the minus sign as well, and I’m sure any math teacher would agree (the ones over here anyway, but I can’t comment on what is being taught in other places)
edit: I tried, but couldn’t find any source that would claim that -3^2 is the same as (-3)^2. Plenty of references for -3^2 being -9 though
Even if you are taught that -3^2 = 9 in some parts f the world, I would say that it is far more common to be taught that it is -9.
Because values inside parenthesis must be solved before they can be used to find a solution to the equation, since (-3) is already solved as -3, then the brackets here are completely unnecessary, but if you like you can use the brackets to clarify the meaning, if the equation requires it, but to assume that -3^2 is -(3)^2 actually changes the value of -3^2, so it is a bad habit to form IMO, I am self taught btw.
Wouldn’t this mean that the parenthesis in -(3)^2 is also already solved as 3, and thus the parenthesis can be removed?
One last point. How would you draw the function -x^2
Sure if you willing to rewrite the equation as -1*3^2 but parenthesis look much cleaner
Wait you mean ƒ(x) = -x² ???
yes, that’s what I mean
In the exact opposite of x², hence the negative symbol.
-3^2 = 9 since the square root of -9 does not exist.
However, you also said this:
-x*-x is always positive for real values of x, thus by your reasoning -x^2 would look identical to x^2
edit: I just realized that even your reasoning that -x*-x=-1(xx) is wrong.
(-1x)(-1x) is not -1(xx)
Didn’t think of that, but technically speaking the square root of any negative number does not exist since any negative number times itself is always positive, how to resolve this conflict!
whoops your right, fixing