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เข้าร่วมเมื่อ 18 ส.ค. 2024
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Euler formula is simply wrong. One side is the exp function which tends to infinity and the other side is a sum of 2 trig functions each ranging from -1 to 1, ie it's finite. So, these 2 sides can't be equal.
Euler's equation is well established. When the exponent of e is purely imaginary as it is here, the result has a magnitude of 1, and simply spins around the origin in the complex plane, not tending to infinity. Complex numbers are weird and unintuitive. Imaginary exponents are tough to wrap your head around.
@immovableobjectify Euler formula was derived by setting iθ in the exponent Taylor series. Right? But that exp series was validated for real numbers, not for imaginary numbers. So, using it to derive the formula was simply erroneous. And I described why it is erroneous. Try to understand it.
Two variables in one equation can not be solved separately.🎉🎉
Okay Boss 🙂
писят два
1/14+1/(14×13)=1/13 則14+182=196
your answer is one of the infinitely-many values. this is because -1 = exp[i*(pi + 2*pi*n)] where n = ...,-2,-1,0,1,2,... therefore, the final answer is exp[i*pi^3/2 (1+2*n)] where n = ...,-2,-1,0,1,2,...
You need to write the pi symbol more clearly as it often appears as though you are writing the variable x!
Okay 👍
438
-3 y. Course y -1 √>>t =202 D
how do you just manage to come up with 1681 as a factor in ur brain? is there any sort of way to find a factor of numbers give you a proper set? plz help
As we have to get a commen factor like (b+41) to simplify the solution by simple inspection, And as we know that 41×41 is equal to 1681. Therefore, while taking 41b and 1681 into factorizing taking out 41 commen...it will be giving desired factors. Hope you got it😌
A questão é interessante, mas é preciso especificar melhor até que ponto deve- se resolvê-la. BRASIL Dezembro de 2024.
Alright Boss 😊 Thanks for sharing your precious feedback 😌
Could have gone straight from 2:52 to 4:46 without losing anyone.
How i root of i = 4.81
Too slow in writing.😂
Yeah The exponents are in the way that can't be written fast...and it may cause any missunderstanding.
You can watch it on 2x speed🤗
hold down left click, very useful
It's tedious to write the same expression over and over again.
@@xbia1 I agree, it breaks the flow.
Решил за 25 секунд Ответ: e^(π/2)
You are brilliant 😍
I think this question is wrong I = exp(I *[pi/2 +2npi] ) So 1/I pow Gives Exp(pi/2*[1 + 4n]) So many boobs and noobs I the exponent 😊
Really use less
Okay😞
when I studied math, this was called rationalizing. And since you know where you want to go, don't go thru all this. Once you place everything under the 5th root. multiply them by 8/8 and be done with a rational denominator 2.
Alright Boss
{2+4}=6 2^3 (x ➖ 3x+2).
1/(20)+1/(21)=1/41 /(10)+/(10^11) /(5^6) /(5^2^3)/(2^3^1^1) (2^3) (ab ➖ 3ab+2).
How to know to add 169
To make perfect factors 😉
Hello ,everybody ! Greetings! Thanks , respects and considerations to all of you ...! Let me say that , here everything is just wonderful but uncomplete ( sorry to underline) !!! We have an infinity of solutions for this equation ( or equality ) . Let : a not null , b not null, k not null ,1/a+1/b=1/13 and a=k*b (or b= k*a) . Solving the system : 1/a+1/b=1/13 and a=k*b we get : 13(a+b)=a*b 13(k*b+b)=k*b*b 13(k+1)b- k*b*b=0 b(13*k+13-k*b)=0 and b not null 13*k+13-k*b=0 From here , let find k K*b-13*k=13 K=(13)/(b-13) Fron there: a =k*b=(13b)/( b-13) b not egal to 13 , b >0 and a>0 , that means that b belongs to the interval ] +13; + infinity [ Now for any b belonging to the given interval we have : a+b=b(k+1)=( b*b)/(b-13) Thanks ! Fron a former African and Senegalese Student in Moscow, Russia!
Great effort and brilliant approach Boss 🙂 Thanks for sharing your precious feedback 😌
x^6/729=1(x ➖ 1x+1).
(5 ➖ 2)^2^3 (2^3 ➖ 1)^1^1^1 (2^3) (x ➖ 3x+2).
(x^6+18)=18x^6 3^6x^6 3^2^3x^2^3 1^2^1x^1^3 2x^3 (x ➖ 3x+2).
(2)+(2)=4(y ➖ 2x+2). 4^4 2^2^2^2 1^2^1^1 21(xy ➖ 2xy+2).
Just use the exponential form and divide the exponent by 2 😁
Alright Boss 😊
(x ➖ 1ix+1i).
So the answer to a meaningless problem is something so beautiful!!!😋
Yess boss
What is the purpose for the step of multiplying and dividing by 2?
To make the power positive and to get a simpler answer 😊
I understand that now. Thank you!
Nice
Thanks 😊
A+b 82
You are right. But its not only solution.
분모통일시키면 ab=13 a+b=1바로나오자나 a=1-b b(1-b)=13 -b^2+b-13=0 이차방정식풀어서 b값 뽑으면 끝아님?
Well explained
Thanks 👍
Define "I" as X Squared. So then the square root of X Squared is X. Answer is X if you define "I" as X^2. But that is just not making the assumption that "I" means imaginary number.
But, what is the point of the "solution". You will recurr to the calculator anyway, and the solution is as hard as the problem. Nonsense, to me.
Okay Boss Admit it 😔
Mathematica gives this, 0.0000255089026236085942824535846310. Excel gives right the first 18 decimals. Is the answer of the vid.
Answer of vid is not in decimal number...its just simpler form of original expression without using calculator 😌
@@MathBeast.channel-l9i Of course. There was a comment asking if 0.000025 etc. was correct, may be that person was confusing about it. I tried to put clear, as I said in my comment that the value is the same. In decimal form is less precise, yes.
Thank you professor for good solution.
You are welcome 🤗
You do realise, right, that the problem can be solved in 10 seconds?
Okay Boss
Beautiful
Why not cancel the power on both sides X/3 = 2 X = 3*2 = 6 Check (6/3)⁶ = 2⁶ = 64 Done
You are right But it has one more real solution and 4 complex solutions also 😊
@@MathBeast.channel-l9i there is paper about what is equation . The complex solution sometimes doesn't justify the equation. In short, sometimes simplicity is just the best .
Класс
🤔
asnwer= a+b=15 isit
asnwer=1764 isit
Yes You are right 👍
No
PRINCIPAL ROOT: 64 = 2^6 (x/3)^6= 2^6 x/3 = 2 x = 6 OTHER ROOTS: degree 6 polynomial, therefore we should convert this into Polar and rotate by π/3 so: 6∠0, 6∠π/3, 6∠2π/3, 6∠π, 6∠4π/3 and 6∠5π/3 are the solutions! if ya want rectangular just use rcos(θ) + i*rsin(θ), for r∠θ ±6 and ±3±3i√3
can we assume that if there is even power (same) on both LHS and RHS as in this case '6' then whatever will be value of x then it always well have same value in negative? Like on solving value of x was 6 so can we assume since it had even power(6) then it also will have same value but in negative(-6)? without actually solving the equation?
Thanks for sharing your kind review
I will be posting my review about your suggestion in while 🙂
ASNWER=4
asnwer=/3+-/3/3 isit
Yes.
But it have more solutions too. Total six solutions Two real roots And four complex roots
No... It should be 6. -+6
x/13+y/13=1/a+1/b x+y=1 x/13=......
0.5/13+0.5/13=1/a+1/b
Minus sign should be plus in next to last step
You are right 👍 I'm really sorry 😔 That's typo.
Your solution seems right. In fact, e (exp) pi/2 is a real number 4.810495. This number appears intuitively very strange. Can you please provide a proof that this solution is correct?
14
8:36 . . . (-2)(-23814) = +46368
(5^(1/2)-2)^8. let 5^(1/2) = a & 2= b then equation become (a-b)^8=[{(a-b)^2}^2]^2= [{(5^(1/2)-2)^2}^2]^2 using (a-b)^2=a^2+b^2-2ab {(5+4-4[5^(1/2)])^2}^2 {(9-4√5)^2}^2 again (a-b)^2=a^2+b^2-2ab (81+80-72√5)^2 (161-72√5)^2 using (a-b)^2=a^2+b^2-2ab (51841-23184√5)
Nice Approach 👍