Challenging Exponential Equation | Solve (x)^x^2=(x)^1/x. || Exponential Equation With Same Basis

[@劉俊良-t5y]

謝謝！

[@letstalkwithbigsheila]

You are doing well

[@onlineMathsTV]

Smiles. Thanks for the comment my able mistress. Much love from all of us @OnlineMathsTV.....😍😍😍

[@paulmiddletonphotography4368]

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.

[@Rkap_Oz]

Wew, outstanding

[@usmanudadda99]

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

[@onlineMathsTV]

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.

[@Frank-kx4hc]

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: kzbin.info/www/bejne/l3illmyFl9afraM

[@userr717]

I'm from Bangladesh . Thank you for teaching .

[@onlineMathsTV]

You are most welcome ma. Thanks for watching our contents and dropping a comment as well. We all @Onlinemathstv love you dearly💖💖❤️❤️💕🙋🙋🙋

[@kylekatarn1986]

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

[@chuksnonso2320]

On point 👨

[@onlineMathsTV]

Thanks sir.

[@BrightBrainIntegral]

Nice work from OnlinemathsTV

[@onlineMathsTV]

thanks sir/ma

[@Aritely]

4:19 Division by 0, 14:13 checking

[@Kovaljov6691]

0^0 = 1 😮

[@danielfranca1939]

Great

[@onlineMathsTV]

Thanks for the comment ma. Much love ❤️❤️❤️

[@habeebalbarghothy6320]

From the bigining x^2=1/x X^3=1, so x=1

[@StephieJoseph-io3wt]

Nice

[@onlineMathsTV]

Thanks

[@physicguy92093]

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)

[@onlineMathsTV]

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.

[@comdo777]

asnwer=1 x isit 🤣😂😅

[@onlineMathsTV]

😍😍🤣🤣🤣😂😂😂🤸‍♂️🤸‍♂️🤸‍♂️ Thanks for this comment sir. Much love ❤️❤️❤️💕💕

[@jayanthkolisetti5353]

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.

[@dusanpokorny329]

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.

[@prime423]

If the bases are the same,the exponents must be equal!!This is then trivial.

[@syedmdabid7191]

What's the meaning of Wn(2) ????? Its Value= ???

[@syedmdabid7191]

The base is the same and so x^2= 1/x, so, x= (1) ^1/3= l responsi, solutio realis.

[@rajd7614]

14:58zero to the power zero is One NOT ZERO

[@onlineMathsTV]

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.

[@rajd7614]

kzbin.info/www/bejne/qGHCnpxuo8yBpK8 " 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"

[@tyronekim3506]

​@@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 KZbin. Good luck.

[@manuelnevessilvaneves2311]

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

[@kksomdr]

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.

[@Fl0wGuyz]

I thought -1 was also a solution for x

[@jidraffgithendu7546]

Anything raised to power 0 is zero. So both sides are 0

[@alibenali7397]

Please,don't forget that:x^x^2=(x)^(1/x) has no definition if :x=0 !

[@onlineMathsTV]

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...👍👍👍

[@Wangkheimayum421]

0⁰ is not 0

[@onlineMathsTV]

Yes, u are right

[@JSSTyger]

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).

[@Yes_I_c4n]

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?

[@onlineMathsTV]

X=0, is extraneous

[@daacosta]

x can't be zero

[@prime423]

Zero is NOT a solution!!Try it in the original equation!!

[@Frank-kx4hc]

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: kzbin.info/www/bejne/l3illmyFl9afraM

[@onlineMathsTV]

Nice, I just watched the video clip...very helpful sir. Thanks for sharing this with us. Much love....❤️❤️💖💖💖