A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
Rules
This is a science community. We use the Dawkins definition of meme.
The number of solutions/roots is equal to the highest power x is raised to (there are other forms with different rules and this applies to R and C not higher order systems)
Some roots can be complex and some can be duplicates but when it comes to the real and complex roots, that rule generally holds.
This only ever got handed down to us as gospel. Is there a compelling reason why we should accept that (-3) × (-3) = 9?
You can look at multiplication as a shorthand for repeated addition, so, for example:
3x3=0 + 3 + 3 + 3 = 9
In other words we have three lots of three. The zero will be handy later...
Next consider:
-3x3 = 0 + -3 + -3 + -3 = -9
Here we have three lots of minus three. So what happens if we instead have minus three lots of three? Instead of adding the threes, we subtract them:
3x-3 = 0 - 3 - 3 - 3 = -9
Finally, what if we want minus three lots of minus three? Subtracting a negative number is the equivalent of adding the positive value:
-3x-3 = 0 - -3 - -3 - -3 = 0 + 3 + 3 + 3 = 9
Do let me know if some of that isn't clear.
This was very clear. Now that I see it, I realize it’s the same reasoning why x^(-3) is 1/(x^3):
2 × -3 = -6
1 × -3 = -3
0 × -3 = 0
-1 × -3 = 3
Thank you!
Middle school math memes
-3 feels like cheating.
Eh, not really. It's been a while, but I'm pretty sure the rule in algebra when solving for a squared variable like this is to use ± for exactly that reason.
Doesn’t x also equal -3?
Sqrt(9)
Uhm, actually 🤓☝️!
Afaik sqrt only returns positive numbers, but if you're searching for X you should do more logic, as both -3 and 3 squared is 9, but sqrt(9) is just 3.
If I'm wrong please correct me, caz I don't really know how to properly write this down in a proof, so I might be wrong here. :p
(ps: I fact checked with wolfram, but I still donno how to split the equation formally)
You're correct. The square root operator only returns the principal root (the positive one).
So if x^2 = 9 then x = ±√9 = ±3
That's why in something like the quadratic formula we all had to memorize in school its got a "plus or minus" in it: -b ± √...(etc)
x^2 = 9
<=>
|x| = sqrt(9)
would be correct. That way you get both 3 and -3 for x.
That's the way your math teacher would do it. So the correct version of the statement in the picture is: "if x^2 = 9 then abs(x) = 3"