China | Can you solve this? | Math Olympiad | find k!!

China | Can you solve this? | Math Olympiad

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Explore the interesting world of exponential equations with varying bases and unlock the power of exponentiation! In this educational video, we delve into the concept of exponential equations where the base is not a constant value. Learn the fundamentals, discover the properties, and master solving equations with different bases, all explained clearly and concisely. Join us on this exponential journey and level up your mathematical prowess!

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[ivanmusenko]

I was needed only 2 seconds to find out that "2" is the only answer

[HarinamKumar-iomc]

K•k•k+k=10
K=? Easy question
K=2 by easy solution
I am from Bharat🇮🇳

[拗拗拗拗]

It’s simple to find 2, but there might be complex solutions, so solving this equation like in the video is the college way.

[triwahyu]

Kakak pertama itu broo🤣👍
Ilmu H20..huruf jawa 20 hurup itu lintang utara selatan 0 20 40 60 80..01.11 11
Menuju Dunia lain 👍🙏

[hongphuc]

*k^3-8+k-2=0*
*(k-2)(k^2+2k+4)+(k-2)=0*
*(k-2)[(k^2+2k+4)+1]=0*
*k=2 k=(-1±2i)*

[MNH.z]

Để giải phương trình
K×K×K+K=10, ta làm như sau:
1. Đặt phương trình:
𝐾^3+𝐾=10
2. Chuyển vế phương trình:
K^3+K−10=0
3. Giải phương trình này bằng cách thử các giá trị của 𝐾
*/ Nếu 𝐾=1
=> 1^3+1−10=1+1−10=−8≠0

*/ Nếu 𝐾=2
=> 2^3+2−10=8+2−10=0
Vậy:
K=2 là nghiệm của phương trình

[carlosmancosanchez]

Thank you. Greettings from Medellín. Take care

[walterwen]

k^3 + k = 10 = 2(5) = 2(4 + 1)
= 2^3 + 2; k = 2
Two complex value roots;
k^2 + 2k + 5 = 0
k = - 1 +/- 2i

[gilberttessa]

k³+k=10
k(k²+1)=(2)(5)
k=2 or k²+1=5

We have only solution k=2

[gonzalezxelhuaeric]

Excelente vídeo, muy buena explicación 😊

[Nazimİsmayılov-eu]

Olimpiada üçün çox sadə məsələdir.Belə saytlara ancaq riyaziyyatdan anlayışı olanların baxdığını nəzərə alsaq kiçik detalların izahına çox vaxt sərf edirsiniz.Siz də, saytların demək olar ki, hamısında kvadrat tənliyə gətirilən məsələləri ancaq eyni düsturla həll edirlər, halbuki burada çevrilmiş kvadrat tənliyin kökləri düsturu ilə həll etmək daha əlverişli idi.Sağ olun.

[amtrakatsfnyc]

Using the Rational Root Theorem and synthetic division is a method that is more efficient and can be applied for all polynomial equations. What would logically motivate a person to use 8+2=10?

[YAWTon]

Cubic equation with a first obvious root k=2. Divide by (k-2) and solve the resulting quadratic equation to obrain the two additional complex solutions.

[dany]

Essayez de trouver un raisonnement plus compliqué .

[lembusora]

k³ + k = 10
k³ = 10 - k
k². k = 10 - k
k² = (10 - k) : k
k²= 10/k - 1

[MrKovalius]

If you guess that 10 can be expressed as 8+2, you might as well guess that the solution is 2. You have to move everything to one side to get a polynomial equation. Then you can guess the rational root and use Bezoute's theorem to determine if there are other roots.

[rockfan]

A minor good calculation. Better is:
k * (k'2 + 1) = 10 and as 10 = 2 * 5 you see directly that k = 2 is a solution

[GeorgeAlexanderOz]

You didn't show a real solution, because you chose 10=8+2 only because you already knew the solution. So that is circular. Why didn't you choose 10=7+3 as a starting point? Try to show a solution for k x k x k + k = 11.5

[amalbanerjee]

Please don't go through complicated way.