Math Olympiad Solution.
ฝัง
- เผยแพร่เมื่อ 27 ก.ย. 2024
- I will tutor you on how to solve this type of math Olympiad question with easy following some or few of mathematical rules/laws ranging from indices to algebraic factorization. I advise that you watch this video the first time and for the second time you go for the hidden tricks and practice how to solve it yourself.
Never skip any part of this video clip in order to get the full details.
#matholympiad #onlinemathstv #tutors
Great explaining! Unfortunately you have written a "+" instead of the originally given "-". But except from that everything was right and well explained:)
Excellent explaining man. You are simply amazing. I have become rusty with my Math after about 2 years break from active teaching.
luar biasa sangat membantu,terima kasih
Before I watch this, a quick question:
Are you allowing nonreal (i.e., complex) values? I ask because there are NO real numbers x that satisify the first equation. Why? FACT: For any nonnegative quantity Q (think of x^2 here), Q + 1/Q >= 2! Since root(2) < 2, we have a contradiction. Therefore, whatever you find for the value of the second expression is meaningless!
(A bit later)... You had x^8 = -1... and again, no mention of the fact that x is complex (not real number).
(Full disclosure: I am a PhD mathematician and retired Penn State U. mathematics professor.)
thanks teacher 😇😇
Спасибо. Очень простое и оригинальное решение. Я не владею языком, но все понятно.
Classicccccc !!! Love this channel so substantially
Thanks a million sir/ma
First equation does not have valid answers, if we do not use complex numbers. So the whole problem doesn't make any sense.
It makes sense since we were not restricted to real numbers.
There was no question what is x. No matter if it is complex. It was interesting😊
th-cam.com/video/q7M-TlRioPo/w-d-xo.htmlsi=2m0lBfaGUDsO4EgK
Yep it right when x is a real number but it will be incomplete when x is a complex number. And the question doesn’t have the condition of x so it might right or wrong (My opinion)
Bạn áp dụng các công thức toán học thật tuyệt vời. Nếu tôi biết bạn sớm hơn, tôi học toán sẽ giỏi hơn.👍👍
Brilliant! (last mistake of sign is unimportant of course). I am sure you know that x in first equation is =exp(+-i*pi/8) which makes solving the "2024" question very trivial, but I like also your smart trick. Congratulatins!
Noted sir, I will be more careful and observant in subsequent videos sir.
Thanks for this keen observation sir.
Respect 👍👍👍
What a great explanation
Glad you liked it.
Thanks a million sir
look iam irainian and at Iran usualy we have so meny tests like thie and for this test we have option like (this is imposible) or (x donot have any value) accquaintace with other countries test
Thanks a lot
Super reşenie. On xoroşiy matematik
Well explained.
Thanks sir
Very basic questions for our exams. Turkish exams for studiying university is very difficult. And there are about 30 000 different questions on only math course... this question is one of them...
C'est bien mais il faut être précis dans l'énoncé du problème.
Dans la resolution, utiliser bien les connecteurs logiques .
Excellent 👌
From 4:06, keeping squaring that gives X^8 + X^-8 = 2
Square again the last term: X^16 + X^-16 = 2
and again, it is 2 only.
It means it does not change it after power 8.
Because 2024 is divisible by 8, the final expression answer should be 2.
Can you spot any mistake above?
at 5::15, X^8 + 1 = 0, means x is imaginary number. Why is this answer in the real number??
Correct!
Thanks
Good
But x^8 has no solution or either from equation x^4+1/x^4 has 4 solution
??
Сумма в равенстве слева ни при каких действительных икс не может быть меньше двух. А права стоит корень из двух, который меньше двух. И ЧТО? Мы имеем дело с комплексными числами?
Ans. 0
x²+1/x²=√2
x⁴-√2 x²+1=0
x²=(√2+√2 i)/2=(1+i)/√2
x²⁰²⁴ - 1/x²⁰²⁴
=(1+i)²⁰²⁴/2¹⁰¹² - 2¹⁰¹²/(1+i)²⁰²⁴
=(2i)¹⁰¹²/2¹⁰¹² - 2¹⁰¹²/(2i)¹⁰¹²
= i¹⁰¹² - 1/i¹⁰¹² = 1 - 1 = 0
Last statement?
🙏
If X=0 , Whole thing is meaning less, because 1/0.
friend last line has a mistake -sign should take the + sign at end of problem
If you graph the first equation in x^2 you have no real solutions. If you substitute p for x^2 and solve the resulting quadratic equation for p, you get only complex solutions for p and x.
Solving the quadratic gives x=(2^1/2+i×2^1/2)/2 or x=(2^1/2-i×2^1/2)/2. Either solution gives x^8=-16, so how does x^8=-1?
we are not restricted to real nubers@@HeywoodUmanoff
it in not exist for real numbers
Дано: найти разницу. Ответ пишем для суммы. Что?
Por qué colocaste signo más al final?
it is not suppose to be. It is an error on my part sir.
Pardon me pls 👍👍👍
Iast step error of + sign.
X value is equal by/ 25/0
I do not get your point here sir, kindly rephrase it sir.
There is a mistake in the question. X²+1/x²=2 not root of 2 this is the right
Solution of the two problem is x=1
Thanks for this observation sir
0 = (-1 - {-1}) ; x = (i^{1/4})
0..., really ?
As answer to 0 bother me .
わざわざ計算したのに結果0か...。
You cant find the value of x
it is imposinle
final equation is wrong !
not plus
please X^4x4 is x^16
X⁴×X⁴ = X⁸ brother
Thanks man, but I think you can’t multiply by variable …….variable to power four?
Noted but I will do my research on that and get back to you on this point sir.
Thanks for the keen observation....👍👍👍
You can, as long as that variable is not 0.
암삼 10초컷
Это глупость, которую смешно смотреть
Really? That is well said Prof, hahaha...
why is the right way to do math so dumb why cant i just multiply the square root of 2 with x^2 and then have x+1=2x then subtract 2x from both sides and get x^2-2x+1 which if you plug to quadratic formula it equals 2 plus or minus 0 /1 which is 2 and then plug that in
Answer: 0
😂😂
how xxxxxxxx times can be -1 only if you put{ i} the phantom
Le faux entraîne le faux
Really?
Haiz find x : (x²)⁴=-1
4 is pronounced for not fur.......very irritating accent!
Was that all you could hear from the whole video? You need rehabilitation ASAP!
Спасибо. Очень простое и оригинальное решение. Я не владею языком, но все понятно.
UNDERSTANDING...
IS BRAVERMAN PART OF THE "PLOT'?
BRAVERMAN: BUDGET WASN'T ENOUGH
CATHOLIC CHURCH OF THE ARCHANGELS GADUWA, DURUMI, ABUJA.
Спасибо. Очень простое и оригинальное решение. Я не владею языком, но все понятно.
It's 0 but i did it in a much harder tehnic tho
Yes. No solutions.
And finaly not plus, but mines.
Too fetaled
Curioso y divertido el problema... Genial.
Thanks for the math teaching.It was amazing 😊😊😊😊😊😊😊😊😊😊
x^8 = -1 obviously x cannot be a real number. You didn't even mention that.
At last wrong replacement
Это уравнение не имеет смысла, так как не было поставлено в каких величинах мы решаем, если в натуральных, то x^8 не равняется-1. Так что надо решать в комплексных числах, а там уже проще просто корни найти x через замену и обратную постановку, но так красивый ответ не получится
Oops
Reponse=0
C’était + ou -?
Почему когда получаем x^8=-1 мы продолжаем решать? Разве может число в 8й степени быть отрицательным?
Да может быть только в комплексных числах. К примеру уравнение х^2=-1 имеет два решения x=i и x=-i. А уравнение х^8=-1 имеет 8 решения одно из каторых x=e^iπ/8
@@ffch999 спасибо огромное!!
@@ТимаПоваров Спасибо Вам тоже
Very nice
Excellent explanation. Thank you.
Glad it was helpful!
Thanks so much for watching and encouraging us with this comment sir.
❤😊
хотя не знаю языка, все было понятно Спасибо
Thanks for watching even though you do not understand the language. The language is English.
Above all we are glad you got a thorough understanding of the procedure sir.
Much love from Nigeria the heart bit of Africa...💖💖💕💕💕
良問やなあ
thanks for the acknowledgement sir.
Well done
Thanks my good friend for this observation.
8×256=2048 not 2024😂
8x253@@cocking2.198
9:04 a very complicated problem added to your complicated way of solving it.
Unfortunately your efforts are meaningless
you wrong. is not 253 but 256