A Nice Olympiad Math Algebra Equation | Can you solve for x?

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Find the value of x?
How to solve x^5 - 1 = 0

In this video, we'll show you How to Solve Math Olympiad Question A Nice Algebra Problem x^5 - 1 = 0 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[usmasuda]

Use a complex plane, which is much easier.

[zawatsky]

1:57 - не по правилам! (x+1)(x³+x+1)=0. x=-1 ∨ x³+x+1=0.

[Sreberko_s]

My stupid ass immiedietely thought of 1

[sammurphy]

Just use De Moivre’s Theorem. Much easier and much quicker.

[bluesky]

x^5-1=0, x^5=1, x^5=exp(i*2*pi*n) where n=0, 1, 2, 3, 4. x=1 for n=0, x=cos(2*pi/5)=i*sin(2*pi/5) for n=1,

[sinanfr]

It was not said that the domain will be R or C

[ben-rip]

Euler made this problem easy by noting that 1=e^{2ijπ}, where e is Euler's number, π is the ratio of circle circumference to diameter, i=√(–1), and j is any integer.
For x^n=1=e^{2ijπ}, n any positive integer, the n roots would be given by x_j=e^{2ijπ/n}=cos(2jπ/n)+i*sin(2jπ/n), j=0, 1, ..., n–1
For x^5=1=e^{2ijπ} we have x_j=e^{2ijπ/5}=cos(2jπ/5)+i*sin(2jπ/5), j=0, 1, ..., 4, which are easily evaluated using a pocket calculator.