I really like your exhaustive derivations and your pace, not labouring equation manipulation basics, unlike so many others. For those who commented about the solution of x being restricted to the real domain, this restriction was not imposed on the original question and so all solutions are sought. X=0 is a tricky one certainly! Great presentation and teaching! Thank you for all your passion and effort to help many.
Thanks so much sir. You are so lovely for encouraging and supporting OnlinemathsTV on every sides. We pray for more financial breakthrough in your businesses and life endeavors sir. We never forget this great favor you showed to us sir. We love you without mincing words sir...💕💕💖💖❤️😍😍
of course just by looking at x^(1/x), you can write it as x-root of x. Since x works as an index, it should be a natural number only. So if we work on a restricted set (real numbers), x must be positive and integer, so only 1 would be acceptable. The complex zeroes that we found... mmm I don't know if we can accept them, even if we work on the set of complex numbers, mmmm... EDIT: Mmm, I think X can be a fractional rational number. For example: if X=-2/3, we have X^(1/x)= (-2/3)^[1/(-2/3)]=(-2/3)^(-3/2)=square root of [(-2/3)^(-3)]=square root of [(-3/2)^3]. Damn if all of this can be really complicated sometimes XD
In R, the solutions are: -1 and 1. This equation is equivalent to : X^p =1 where base X=x , exponent p=x^2-1/x • X=1 and p in R : x=1 solution, • or X=-1 and p EVEN: x=-1 solution bcse p=1+1=2 EVEN. • or p=0 and X0: x=1 solution. See this trick here: ua-cam.com/video/aGBe9ObqlwA/v-deo.html
Porovnám exponenty. Pak z rovnice vyjde x^3=1 . Jeden kořen je reálný x1 = 1...v komplexní rovině je to jeden z vrcholů rovnostranného trojúhelníka v bodě (1,0). Zbylé vrcholy najdu ve 2. a 3. kvadrantu Gaussovy roviny podle Pythagorovy věty a funkce tangens. Jinak 0^0 není korektní, takže 0 není kořenem rovnice.
3:55 sir 0^anything is 0 , well if we let the limit (x and y aproaches 0) x^y =1 , so for some poeple 0^0 is undefined but it is not wrong for some others to say 0^0=1 ( this has nothing to do with the equation just some opinion of mine wich i would like to seeyour respond)
Thanks a million @Arnaldo5598 for dropping your take on this controversial mathematical expression sir. From my research on 0^0, it is has be proven beyond reasonable doubt that this is undefined.
Yes, that answer, zero is extraneous in this exponential equation hence I asked viewers to drop their own view point/s here. Thanks for this keen observation sir...👍👍👍
x is equal to 1 sir , since bases are same we can cancel them, now we will get x^2=1/x, it is equal to x^2=x^-1, 0 is not possible , we will put 1, when we will put 1 it will satisfy the equation.
ua-cam.com/video/r0_mi8ngNnM/v-deo.html " Dixi " Dixi, a Latin expression, literally translated as "I have spoken". When used, it usually means: "I have said all that I had to say and thus the argument is settled"
@@rajd7614 I clicked on the link and saw the video. The guy determined 0^0 = 1 by using calculators. This is in error, because 0^0 = 0×0 does not equal 1. So, 0^0 is undefined. Don't use quotations to settle controversies in science and mathematics. Don't believe everything you see on UA-cam. Good luck.
But X = 0 does not belong to the domain of the function, as you cannot divide by zero... Thus, X=0 can never be a solution. When X approaches zero, indeed 1/X goes to inf., but that's when X approaches zero, it can never actually be zero. So X=0 is excluded. But indeed zero to the power of inf, is equal to 0 just the same. Also, what about X=-1? It is also a solution to the equation... Where did we miss it?
In R, the solutions are: -1 and 1. This equation is equivalent to : X^p =1 where base X=x , exponent p=x^2-1/x • X=1 and p in R: x=1 solution, • or X=-1 and p EVEN: x=-1 solution bcse p=1+1=2 EVEN. • or p=0 and X0: x=1 solution. See this trick here: ua-cam.com/video/aGBe9ObqlwA/v-deo.html
Wew, outstanding
You are doing well
Smiles. Thanks for the comment my able mistress.
Much love from all of us @OnlineMathsTV.....😍😍😍
I really like your exhaustive derivations and your pace, not labouring equation manipulation basics, unlike so many others. For those who commented about the solution of x being restricted to the real domain, this restriction was not imposed on the original question and so all solutions are sought. X=0 is a tricky one certainly!
Great presentation and teaching! Thank you for all your passion and effort to help many.
On point 👨
Thanks sir.
謝謝！
Thanks so much sir.
You are so lovely for encouraging and supporting OnlinemathsTV on every sides.
We pray for more financial breakthrough in your businesses and life endeavors sir.
We never forget this great favor you showed to us sir.
We love you without mincing words sir...💕💕💖💖❤️😍😍
of course just by looking at x^(1/x), you can write it as x-root of x. Since x works as an index, it should be a natural number only. So if we work on a restricted set (real numbers), x must be positive and integer, so only 1 would be acceptable. The complex zeroes that we found... mmm I don't know if we can accept them, even if we work on the set of complex numbers, mmmm...
EDIT: Mmm, I think X can be a fractional rational number. For example: if X=-2/3, we have X^(1/x)= (-2/3)^[1/(-2/3)]=(-2/3)^(-3/2)=square root of [(-2/3)^(-3)]=square root of [(-3/2)^3].
Damn if all of this can be really complicated sometimes XD
Since X=X (the base)
Then equate x^2 to 1/x, this will simplify to: x^3-1=0.
X^3 =1
x= 3√1
x =1
with that method/approach of urs u will only get one root instead of two hence this approach in this video is most appropriate sir.
In R, the solutions are: -1 and 1.
This equation is equivalent to :
X^p =1 where base X=x , exponent p=x^2-1/x
• X=1 and p in R : x=1 solution,
• or X=-1 and p EVEN: x=-1 solution bcse p=1+1=2 EVEN.
• or p=0 and X0: x=1 solution.
See this trick here:
ua-cam.com/video/aGBe9ObqlwA/v-deo.html
I'm from Bangladesh . Thank you for teaching .
You are most welcome ma. Thanks for watching our contents and dropping a comment as well.
We all @Onlinemathstv love you dearly💖💖❤️❤️💕🙋🙋🙋
Great
Thanks for the comment ma. Much love ❤️❤️❤️
4:19 Division by 0, 14:13 checking
Nice
Thanks
The function has 2 roots X=0,7 and x= 1. The value x=0 is no root Sorry FOR X=O the value of the function is 1
Nice work from OnlinemathsTV
thanks sir/ma
0^0 = 1 😮
From the bigining x^2=1/x
X^3=1, so x=1
Porovnám exponenty. Pak z rovnice vyjde x^3=1 . Jeden kořen je reálný x1 = 1...v komplexní rovině je to jeden z vrcholů rovnostranného trojúhelníka v bodě (1,0). Zbylé vrcholy najdu ve 2. a 3. kvadrantu Gaussovy roviny podle Pythagorovy věty a funkce tangens. Jinak 0^0 není korektní, takže 0 není kořenem rovnice.
3:55 sir 0^anything is 0 , well if we let the limit (x and y aproaches 0) x^y =1 , so for some poeple 0^0 is undefined but it is not wrong for some others to say 0^0=1 ( this has nothing to do with the equation just some opinion of mine wich i would like to seeyour respond)
Thanks a million @Arnaldo5598 for dropping your take on this controversial mathematical expression sir.
From my research on 0^0, it is has be proven beyond reasonable doubt that this is undefined.
Please,don't forget that:x^x^2=(x)^(1/x) has no definition if :x=0 !
Yes, that answer, zero is extraneous in this exponential equation hence I asked viewers to drop their own view point/s here.
Thanks for this keen observation sir...👍👍👍
x is equal to 1 sir , since bases are same we can cancel them, now we will get x^2=1/x, it is equal to x^2=x^-1, 0 is not possible , we will put 1, when we will put 1 it will satisfy the equation.
The base is the same and so x^2= 1/x, so, x= (1) ^1/3= l responsi, solutio realis.
What's the meaning of Wn(2) ????? Its Value= ???
If the bases are the same,the exponents must be equal!!This is then trivial.
X^(1/X) => X is not 0.(No definition). Both sides base is equal. Therefore X^2 = 1/X. X^2 - 1/X = 0. X^3 - 1 = 0. (X - 1)(X^2 + X + 1) = 0. Therefore X = 1. X^2 + X + 1 = 0.
14:58zero to the power zero is One NOT ZERO
Zero to the power of zero is undefined; that means the expression on the LHS is not equal to that on the RHS. I forgot to cross the equality sign.
ua-cam.com/video/r0_mi8ngNnM/v-deo.html
" Dixi "
Dixi, a Latin expression, literally translated as "I have spoken". When used, it usually means: "I have said all that I had to say and thus the argument is settled"
@@rajd7614 I clicked on the link and saw the video. The guy determined 0^0 = 1 by using calculators. This is in error, because 0^0 = 0×0 does not equal 1. So, 0^0 is undefined.
Don't use quotations to settle controversies in science and mathematics.
Don't believe everything you see on UA-cam. Good luck.
According to a modern interpretation of a^b^c, it is evaluated as (a^b)^c, in which case x^x^2 = (x^x)^2 or x^(2x).
I thought -1 was also a solution for x
But X = 0 does not belong to the domain of the function, as you cannot divide by zero... Thus, X=0 can never be a solution. When X approaches zero, indeed 1/X goes to inf., but that's when X approaches zero, it can never actually be zero.
So X=0 is excluded. But indeed zero to the power of inf, is equal to 0 just the same.
Also, what about X=-1? It is also a solution to the equation... Where did we miss it?
X=0, is extraneous
Anything raised to power 0 is zero. So both sides are 0
asnwer=1 x isit 🤣😂😅
😍😍🤣🤣🤣😂😂😂🤸♂️🤸♂️🤸♂️
Thanks for this comment sir.
Much love ❤️❤️❤️💕💕
In R, the solutions are: -1 and 1.
This equation is equivalent to :
X^p =1 where base X=x , exponent p=x^2-1/x
• X=1 and p in R: x=1 solution,
• or X=-1 and p EVEN: x=-1 solution bcse p=1+1=2 EVEN.
• or p=0 and X0: x=1 solution.
See this trick here:
ua-cam.com/video/aGBe9ObqlwA/v-deo.html
Nice, I just watched the video clip...very helpful sir.
Thanks for sharing this with us.
Much love....❤️❤️💖💖💖
Zero is NOT a solution!!Try it in the original equation!!
0⁰ is not 0
Yes, u are right
x can't be zero