Nice Math Olympiad Algebra Equation | How to solve for the value of "x"

[@renesperb]

There is a short way to the solutions : write the equation as x^6=4^6*e^(2 i π k) , k=0,1,2 ...5. Then x (k)=4*e^(i π k)/3),that is
x(k) =4*(cos(π*k/3)+i sin(π k /3)) .For k=0 ,e.g. x(0) = 4 ,x(1) =4*(cos(π/3}+i*sin[π/3]=2*(1+i√3) ,etc.

[@GodbornNoven]

Exactly just use the polar form it would've been easier lmao

[@BhavinBashyal-oj9ij]

isnt the answer just +-4

[@MathBeast.channel-l9i]

4 and -4 are real roots...but it has more four complex roots as shown in video

[@RealQinnMalloryu4]

64/x^3=4 (x ➖ 4x+4).

[@BaraaHadjadj]

X=4

[@NagamaniCherukunuru]

🎉

[@MathBeast.channel-l9i]

Thanks

[@thanjavurvlogs1307]

Can't we apply nth root of complex number formula

[@srecky7822]

That's like saying x = 3 + 1 but with extra steps

[@anorak5773]

so answer is X=4 why is it not simpler to go from x^6 - 4^6 = 0 so X^6 = 4^6 then powers cancel and you get X = 4?

[@leahithink]

because x = 4 isn't the only solution, there is also irrational and complex solutions

[@anorak5773]

@leahithink that's funky !

[@TortoiseMountain635]

bruh X = 4 it aint that hard

[@Adel-m9l]

4 and -4 for real solutions
There's also 4 imagine solutions he mentioned in the video
If x⁶ that means theres 6 solutions ( 2 Real and 4 imagination)

[@MathBeast.channel-l9i]

4 are other complex solutions

[@MathBeast.channel-l9i]

Brilliant response Boss
Thanks 😊