How Many Answers Can You Find? - Advanced Difficulty
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- เผยแพร่เมื่อ 29 ต.ค. 2024
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t^6=2^6
This problem tests understanding of exponential equations and the ability to solve for real and complex roots.
• Competition Level: Math Olympiad (Advanced).
• Grade Level: 11th-12th grade or advanced students.
• Difficulty: Advanced, as it requires solving an equation involving both integer exponents and powers, and understanding of complex numbers.
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My dumbass thought the answer is two then realized it has the power of six so there must be six answers.
Exponentials have only positive solution.
Or we can simple have t^6= 64 (cos 0 + sin 0 i)
T= 2(cos k π/6 + sin k π/6) for 0≤k
very simple
Correct me if I’m wrong but Shouldn’t it be:
T = 2(cos k π/3 + i*sin k π/3)
Also I think you could have made it clearer that k is supposed to be only whole numbers.
I would’ve just written k ∈ {0,1,2,3,4,5}
@@Alex-02 Yes , my bad . you are correct i missed the 2 in the numerator and k being whole ,that makes it more clear for people viewing
Welp at least I got the 2 real numbers correct 🤓
This is not quadratic polynomial.
This is exponential equation and t= 2 only solution.
It has six answers!