How Many Answers Can You Find? - Advanced Difficulty

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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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[@bblunder]

My dumbass thought the answer is two then realized it has the power of six so there must be six answers.

[@AliHassan-hb1bn]

Exponentials have only positive solution.

[@yakomdora5038]

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

[@arkhanok6329]

very simple

[@Alex-02]

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}

[@yakomdora5038]

@@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

[@parrisnia72]

Welp at least I got the 2 real numbers correct 🤓

[@AliHassan-hb1bn]

This is not quadratic polynomial.

[@AliHassan-hb1bn]

This is exponential equation and t= 2 only solution.

[@mathXanswer]

It has six answers!