🔴Nice Square Root Math Problem
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- čas přidán 7. 02. 2024
- Nice Square Root Math Problem
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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 CZcams you will find why it equals 1
As an Algebra beginner, my deepest appreciation!
Excellent
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.
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.
Why a convergent series?
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.
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|
Assume it as x , square both side we get x^2 - 3 = 0 then x = 3
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.
You forgot the part where x is 0. x(x-3)=0 therefore x=0 or x=3
x=0 is not acceptable
Id est 3 responsi
If x^2=3x =>x(x-3)=0
Either x= 0 or x=3
Thx
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.
3
3⁰= 1
3 power 3 and x power 3..power get canceled and answer is 3...simple 😊
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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 ?
3 c option is the answer
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you could take
sqrt(3) x sqrt(3) = 3
and 3 x 3 = 9
and finally take sqrt(9) which is 3
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.
Is the limit of the convergent sequence (a_n) where a_n=3^(1-(1/2)^n). It is lim a_n=3.
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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1
Thanks 🙏
@@bmlogic 3，做错题是常事。
3=x, √3√3... =x, are u shure about that, bcuz 3≠√3√3...
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❤
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.
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
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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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?
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
Can’t see what he’s writing cause of the thumbnail
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😂😂😂😂
First x = √3√3√3√3.. then
X = 3😂😂😂
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I can't understand teacher 😢
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Op
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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
Sol 2.6150
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.
3
X=√.......
X²=3√.......=3X
X2=3X
X=3
I multiplied the √3 by √3 = 3, then 3 x 3 =9, then answer is √9 = 3
Thanks 👍
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
Esto esta mal, eso da 1 ya que 1/ infinito es igual a 0 quedando el 3 elevado a 0 que es 1 ...
Sai ngay từ đặt x, bởi nó vô hạn quá
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3x3x3x3 81
C
Lhs rhs same variable how
En una ecuacion cuadrática hay 2 resultados y aquí solo se buscó uno solo.
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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 don't get it, x × x is 3×3×3..... So infinity???
first u need check it is Convergence
You forgot to check x=0
it cant be zero common sense
Фокусник, блин.
Thanks 🙏
This is similar to how 0.9999999.. = 1 how to find the fraction of such numbers
no
Wrong, ans is 3^7/8, if series trend to infinity then you r right
Jesus loves you so much girl ❤
Thanks 🙏
Nope. Allah is the true God.
I know that the answer is 3, but if it's possible the answer is 3
?^2=3×?
?=3 easy.
C.
Thanks
true but fail solution... can't square a infinite...
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Решение не верное
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utter nonsense
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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
Wrong answer
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с).
Please stop rewriting the problem. Unless u need to soak up more time.
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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
Kuch bhi samaj me nahi aya
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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
Can you solve this ❓👇
czcams.com/video/aCmWWuep4x4/video.htmlsi=nD42kx-uwyKiuqrX
C'est faux
Right but it has 2 solution 0 and 3
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الحل خطأ
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ليش ؟
Respect 😮
y=0 or y=3
are the solutions
Wery nice man
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Very bad
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3
C
3
Thanks 👍💯
3
3
3
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3
3
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C