i find it to be a more complicated than necessary way to go about it. in some countries, that's something you know how to solve before entering highschool. here's a simpler way to go about it: a*a*a = a+a+a a^3 - 3a = 0 a * (a^2 - 3) = 0 using zero product property: "a product equals zero if and only if at least one of its factors equals zero" a = 0 or a^2 - 3 = 0 a^2 = 3 using definition of square root a = sqrt(3) or a = -sqrt(3) Conclusion S = {-sqrt(3); 0; sqrt(3)}
@@iF3lixDE in france, early education is split between (roughly translated) primary school (6-10), "college" (11-14), then "lycee" (15-18). they only slide a year away from their usa equivalents. lycee being the closest equivalent of high school. "college" grades starts with "6eme" and end with "3eme" as you go up into the grades. now what you need to solve that is know what an equation is and know what factorisation is. as early as "4eme" in france you learn both, but don't use them together (though "back in my days" you would already use them together). then in "3eme" you learn to use them together to solve simple quadratic equations with the zero product property. 4eme and 3eme in france are the respective equivalents of 8th and 9th grades in usa. so that would be between last year of middle school and first year of highschool in usa.
The automatic dubbing is activated by default on your channel so if your international viewers do not want to hear some AI voice over your original audio track, they have to change the setting every time manually since YT doesn’t allow viewers to deactivate it and only content creators can do it, I have watched your videos for a while now and it is extremely frustrating to hear the AI dub and am forced to change back the language every single time, more accessibility is not bad per se obviously but it should be not by default and should be the other way around
By the time you get to a(a^2-3)=0, you know one solution is 0. From there, just divide by a, then add 3, then you have the other two solutions. No need to memorize any formulas. Just follow the right steps and use a bit of logic.
a*a*a = a+a+a simplify as a^3 = 3a bring the values to one side a^3 - 3a = 0 factor out a a(a^2 - 3) = 0 difference of squares a^2 - b^2 = (a - b)(a + b) a(a - √3)(a + √3) = 0 The solutions are a = √3, 0, - √3
messy method. if you divide by a variable you have to notify you exclude this variable being equal to 0. and while you do find some solutions, you are not finding all the solutions and you are not proving that you found all solutions.
@@niscent_ The method is fine, only the execution was flawed. Identify and set aside the 0 solution first, seeing easily that 0*0*0 = 0+0+0, then you proceed to find the ±√3 solutions, and it's a cubic so 3 total solutions is the right number.
messy way to write and go through it, leading to errors. also, did you guys never got told to make sure not to divide by 0 when dividing by a variable in an equation? my teacher would have been cursing in disbelief back then. the proper way to go about that a^2 = 3 part is to write either: a = +/- sqrt(3) or to split that square into two equations: a = sqrt(3) or a = -sqrt(3) if you write a = sqrt(3) alone like this you are losing infos here. and then if you conclude with the split between positive and negative solution, that's simply wrong. because the square root is a function, and as such it admits only one output for any given input (sorry i'm not that familiar with the english terms, maybe "image" and "object").
It's impossible that you are teacher. Incredible. You are not explaine correct. So, a³=3a, diveded for a we have a²=3, so a= V3 ....squart root 3,....very simple...and its possible too a = 0
Very nice solution
i find it to be a more complicated than necessary way to go about it. in some countries, that's something you know how to solve before entering highschool.
here's a simpler way to go about it:
a*a*a = a+a+a
a^3 - 3a = 0
a * (a^2 - 3) = 0
using zero product property: "a product equals zero if and only if at least one of its factors equals zero"
a = 0
or
a^2 - 3 = 0
a^2 = 3
using definition of square root
a = sqrt(3) or a = -sqrt(3)
Conclusion
S = {-sqrt(3); 0; sqrt(3)}
> in some countries, that's something you know how to solve before entering highschool. | Yeah, no
@@iF3lixDE in france, early education is split between (roughly translated) primary school (6-10), "college" (11-14), then "lycee" (15-18). they only slide a year away from their usa equivalents. lycee being the closest equivalent of high school. "college" grades starts with "6eme" and end with "3eme" as you go up into the grades.
now what you need to solve that is know what an equation is and know what factorisation is. as early as "4eme" in france you learn both, but don't use them together (though "back in my days" you would already use them together). then in "3eme" you learn to use them together to solve simple quadratic equations with the zero product property.
4eme and 3eme in france are the respective equivalents of 8th and 9th grades in usa. so that would be between last year of middle school and first year of highschool in usa.
Good
The automatic dubbing is activated by default on your channel so if your international viewers do not want to hear some AI voice over your original audio track, they have to change the setting every time manually since YT doesn’t allow viewers to deactivate it and only content creators can do it, I have watched your videos for a while now and it is extremely frustrating to hear the AI dub and am forced to change back the language every single time, more accessibility is not bad per se obviously but it should be not by default and should be the other way around
By the time you get to a(a^2-3)=0, you know one solution is 0. From there, just divide by a, then add 3, then you have the other two solutions. No need to memorize any formulas. Just follow the right steps and use a bit of logic.
a*a*a = a+a+a
simplify as a^3 = 3a
bring the values to one side
a^3 - 3a = 0
factor out a
a(a^2 - 3) = 0
difference of squares a^2 - b^2 = (a - b)(a + b)
a(a - √3)(a + √3) = 0
The solutions are a = √3, 0, - √3
Great 👍
Very nice 👌
Perfect
Lovely explanation ma'am
Nice solution
a^3=3a
a2=3
a=+ or - √3
messy method. if you divide by a variable you have to notify you exclude this variable being equal to 0. and while you do find some solutions, you are not finding all the solutions and you are not proving that you found all solutions.
@@niscent_ The method is fine, only the execution was flawed.
Identify and set aside the 0 solution first, seeing easily that 0*0*0 = 0+0+0, then you proceed to find the ±√3 solutions, and it's a cubic so 3 total solutions is the right number.
Possible values of a=
3a= a.a.a. a^2=3, a=√3, a=(+,-)3//
3a-a^3=0, a( 3-a^2), a=0, a^2-3=0,
+/-3 doesn’t work as a solution, 9=/=27
messy way to write and go through it, leading to errors. also, did you guys never got told to make sure not to divide by 0 when dividing by a variable in an equation? my teacher would have been cursing in disbelief back then.
the proper way to go about that a^2 = 3 part is to write either:
a = +/- sqrt(3)
or to split that square into two equations:
a = sqrt(3) or a = -sqrt(3)
if you write a = sqrt(3) alone like this you are losing infos here. and then if you conclude with the split between positive and negative solution, that's simply wrong. because the square root is a function, and as such it admits only one output for any given input (sorry i'm not that familiar with the english terms, maybe "image" and "object").
0*0*0 = 0+0+0
Quite simple.
Resolução muito longa. Poderia ter acabado na quarta linha.
Excelente
Please... use logarithm, if you do, you can resolve it just behind a bus ticket (base three better for this example)
a^3 =3a; 3= a^2 therefore a = sqrt 3 os the answer
Good evening Mamta Mam.
You lost me when you introduced b
Next time, it would be better if the microphone would be in the same continent as the speaker
It's impossible that you are teacher. Incredible. You are not explaine correct. So, a³=3a, diveded for a we have a²=3, so a= V3 ....squart root 3,....very simple...and its possible too a = 0
Nice solution