🔴Nice Square Root Math Problem
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- Опубліковано 7 лют 2024
- Nice Square Root Math Problem
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![Why you didn't learn tetration in school[Tetration]](/img/n.gif)
Question is whether this is valid. Try to calculate 2 ^2^2... and 4^4^4.... To solve this, you can do the exact same trick
Edit sorry I meant to say x^x^x... = 2 and = 4.
@@matindrie there is a explanation that has the number e involved, i dont remember why x^x^x... = 2 works but x^x^x... = 4 dont, but the trick in the video works, just for some numbers
It has to be bounded, in this case it is clearly < 3. The 2^2^2^2 etc. example diverges, similarly 4^4^4^ etc.
x^...=2
x^...=log_x(2)
2=log_x(2)
x^2=2
x=sqrt(2)
x^...=4
x^4=4
x=sqrt(2)
problem?
@@maxvangulik1988the problem is the fact that you got the same x for 2 different y, thats the whole discussion.
But you can say that using this method results with an optional solution that you still need to verify, and when you actually place sqrt(2) you get 2 so you know that 2 is true and 4 is false.
A way to approach this should be
3^1/2*3^1/4*3^1/8…. Which the infinite some of 1/2+1/4+1/8… equals 1 so 3^1/2*3^1/4*3^1/8…. = 3^1 = 3
Correct me if I’m wrong I’m just a student
You're a student thinking out of the box, or the one who's very good at applying what he already learnt. Believe me you're correct.
How the power becomes 1, can you explain me?🤔
@@MathematicalGalaxy it’s a calculus problem called 1/2^n which if you search it in UA-cam you will find why it equals 1
As an Algebra beginner, my deepest appreciation!
Excellent
x is a number inside the square root
No it isnt
@@Game_Ender4yes it is. which means sqr(3.x) = sqr(3.3) = sqr(9) = 3
Write it down as a convergent series. 3 ^1/(2^n) as n ranges from 1 to infinity. (3^1/2)+(3^1/4)+(3^1/8)+(3^1/16)+.......
which is = 2.999999999.... We will reach 3 as n approaches infinity.
What he has shown is that if the expression has an value, that value must be three. But he hasn't shown that the expression has a value. It might be nonsense.
Think of all the proofs of nonsense that you can get if you assume that 1/0 has a value.
Those "3 dots" at the end always cause problems.
Yes
Yes exactly. The same type of reasoning leads to the conclusion that 1+2+4+8+… = -1
If the sqrt of 3×the sqrt of three twice, then it could be written as 3×sqrt 3 squared. The square root of 3 multiplied by itself would give us back the number 3. When we multiply 3 and 3 and get 9, we can square it to get back 3 which is the answer.
Assume it as x , square both side we get x^2 - 3 = 0 then x = 3
We were unable to see the final steps😂😂
alternatively, the expression can be represented as an infinite product.
x=prod[k=1,♾️](3^2^-k)
ln(x)=sum[k=1,♾️](2^-k•ln(3))
log_3(x)=-1+sum[k=0,♾️](2^-k)
sum[k=0,♾️](x^k)=1/(1-x), |x|
after the step in which he squares both sides we have 3x=x^2. So x=0 or x=3. x=0 is an introduced wrong solution because of the squaring. After squaring both sides of an equation always check for introduced wrong solutions!
Все правильно вы решили,потом отбор корней.х=0 -не подходит по условию или надо было в одз написать ,что не равен 0.Делить обе части можно только на число,при делении на переменную как в ролике так просто делить обе части на х нельзя.Только перенос в левую часть и решение неполного квадратного уравнения.
I think this is an easy way. My first approach before watching the answer was something like-
I tried this with two or three roots of three.
root(3^1+1/2)=root(3^3/2)
roots cancel
= 3^3.
Since the number of roots is non-finite, then it may be that the answer approaches power 1 as we continue.
Tu a choisi x pour le premier terme et tu a simplifié avec un autre terme et qui t'a induit en erreur ou bien c'est voulu ?
Id est 3 responsi
3⁰= 1
3
The answer 7 over 8 which gives the 3 over 7 rooted to 8 attained i. e 3 powered 7 rooted 8 and the answer is (3), thanks.
Is the limit of the convergent sequence (a_n) where a_n=3^(1-(1/2)^n). It is lim a_n=3.
You forgot the part where x is 0. x(x-3)=0 therefore x=0 or x=3
x=0 is not acceptable
Sol 2.6150
you could take
sqrt(3) x sqrt(3) = 3
and 3 x 3 = 9
and finally take sqrt(9) which is 3
3 power 3 and x power 3..power get canceled and answer is 3...simple 😊
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If ? has a value, take p, then by subtitution we also have √(3•p) = p and thus √3√p = p and thus √3 = √p. Hence it has a value p = 3.
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3=x, √3√3... =x, are u shure about that, bcuz 3≠√3√3...
What is written in the final 2 steps? YT has written over it and it's unreadable. Thanks.
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I didn't really have a problem with it. But as I was about to type this I noticed when you go into the comments, the side icons disappear.
@@macbcheesy Does this mean I neefcti access YT in my laptop or desktop? I am on a small iPhone and can't access the comments and the video simultaneously.
@@dalphonhamilton9980 I'm on an android. On the right side of the screen, there isn't a little rectangle with lines? That's where my comments button is.
@@macbcheesyNaw. Thevset up on my iPhone is different. But I do have an Android Kindle. I never use it to access YT. I will try that andcseebif there's a difference. Thanks.
3x=x^2
3x-x^2=0
X(3-x)=0
Either x=0
Otherwise 3-x=0
Therefore 3=x (x=3)
X=3,0 option is 3 so we choose 3
limit issue. There is no way for equalization with zero if you dont accept limit is zero.
3
X=√.......
X²=3√.......=3X
X2=3X
X=3
3 c option is the answer
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1
Thanks 🙏
@@bmlogic 3，做错题是常事。
not true bec:
If the number of 3 root is odd it will be
Different than even number of 3 root.
Odd: 3 root or Multiples of 3 root 3
Even: 3 or multiples of 3.
Thanks I appreciate it
@@saedtrudi1 Sorry didn’t get what you are saying… it doesn’t matter whether the number of ‘root 3’ is odd or even, the result still converge to 3. The problem to the solution is that the solution didn’t prove the value indeed converge to 3 and simply rejected the x=0 solution. Not vigorous though.
@@CutestKyubey.....--.__.__.--b am right
Think about it
The answer:
5) depends
@@saedtrudi1Nope, it approaches 3 the further you continue the pattern.
x²=3x
So x=0
Being a second degree equation, x has 2 possible results: 0 and 3
No there's not the only answer is 3
@@lucifer_morningstar.. yes there is, 0 is a possible answer
@@datboi7395 not in this case since the question can't be zero
@@lucifer_morningstar.. bro do you even know how polynomials work?
Đặt A= bằng biểu thức trên
Ta có A = căn của 3A t làm bth thou❤
Comments are more harder to understand than the video itself😅. Anyway i usually see this kind of qns in civil service exam but i just select an option randomly as i don't know their solving method and don't want to waste time. Now I can actually solve it and choose the answer from as i learnt here❤
Lhs rhs same variable how
3x3x3x3 81
Generalizzazione
. +
x^2 - n x = 0 , n € IN , n € IR
1) x = 0 N.O.K.
2) x = n O.K.
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Did anyone show that the expression even exists or iow that the limit of an with a0 = 3^1/2 and an =(3*an-1)^1/2 exists?
Hint prove it's increasing and less or equal to 3, only then you can set x to (3*x)^1/2
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First x = √3√3√3√3.. then
X = 3😂😂😂
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you have to prove x≠0, or you cannot divided by x
Answer option itself says that it has value, it may be √3, infinity ♾️, 3 or 1. So , we can assume X (×=0)
@@rujrajvee9456doesn't bro what the the options are. You cannot assume that x>0 by looking at options
Options are just answer choices
They doesnt prove what theorem would be applied
They have nothing to do with questions
√(3√(3√(3...))) is always a positive rational number bro.. √3 only gives 1.732..
x² - 3x = 0 gives 2 values.. x = 0 or 3.. but since the above equation will always give a positive rational number, x = 3 is taken..
@@himadrilahiri2778 Nonsense. √3 and √(3√(3√(3...))) are totally different things, you cannot say one is positive so the other is positive. (Should PROVE this relation, don't use feeling or guess)
@@jackshih2262 well, you can solve one step at a time.. √3 gives 1.732, √(3√(3)) gives 2.279, √(3√(3√(3))) gives 2.615, ... similarly, √(3√(3√(3√(3... 3) (20 terms) gives 2.9999.. as you take 100 terms or 1000 terms, the number of 9s in the decimal place increases
Mistake: At first you said x= the triple root
Then on the next step you said x = just a double root so your substitutions were inconsistent and answer was incorrect
Remove this I did not see it was a infinite number of square roots
C
Esto esta mal, eso da 1 ya que 1/ infinito es igual a 0 quedando el 3 elevado a 0 que es 1 ...
I can't understand teacher 😢
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utter nonsense
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first u need check it is Convergence
I don't get it, x × x is 3×3×3..... So infinity???
By your logic it could also be 0 because 3x=x² is equivalent ro 3x-x² whoch can be factorised as x(3-x)=0 so the answers are x=0 or 3-x=0 for 3-x=0 we do -x=-3 we simplify the minus we get x=3
x=0 is not acceptable
Can we get some words on what’s going on? I speak for myself when I says I have no idea what you did at the end of that
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Since it is an infinite pattern, when they squared both sides they got 3*sqrt(3*sqrt3(... the second part had already been defined earlier as x so they could replace it, giving 3x=x^2.
I multiplied the √3 by √3 = 3, then 3 x 3 =9, then answer is √9 = 3
Thanks 👍
I know that the answer is 3, but if it's possible the answer is 3
Can’t see what he’s writing cause of the thumbnail
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Op
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Can you solve this ❓👇
ua-cam.com/video/aCmWWuep4x4/v-deo.htmlsi=nD42kx-uwyKiuqrX
Sai ngay từ đặt x, bởi nó vô hạn quá
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En una ecuacion cuadrática hay 2 resultados y aquí solo se buscó uno solo.
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Jesus loves you so much girl ❤
Thanks 🙏
Nope. Allah is the true God.
This is similar to how 0.9999999.. = 1 how to find the fraction of such numbers
no
Фокусник, блин.
Thanks 🙏
You forgot to check x=0
it cant be zero common sense
?^2=3×?
?=3 easy.
C.
Thanks
C'est faux
Решение не верное
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Wrong answer
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true but fail solution... can't square a infinite...
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Does it actually converge tho?
he literally proofed that
@@crtlallaw no, he just proved if it converges/exists, then 3 would be the value. Those are two different things
Please stop rewriting the problem. Unless u need to soak up more time.
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с).
Wrong, ans is 3^7/8, if series trend to infinity then you r right
Learn math again
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√(3)=3^1/2
√(3.√(3))=√(3.3^1/2)=√(3^3/2)=3^3/4
√(3.√(3.√(3.√...)))=3^((1+2(n-1)/2^n))
n=infini ==> 3^0 ==> 1
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Kuch bhi samaj me nahi aya
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Right but it has 2 solution 0 and 3
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There is the repeating pattern, so you have to see the identity :
x = sqrt(3*x)
so
x² = 3x
x is not equal 0, so
x = 3
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Yes thats what it is
الحل خطأ
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ليش ؟
Respect 😮
Very bad
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y=0 or y=3
are the solutions
Wery nice man
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3
C
3
3
3
Thanks 👍💯
3
3
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3
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C