Nice Algebra Problem. Can you solve this Cambridge Entrance Exam Question?

[@QualityShorts100]

x=1

[@MathmentorX19]

Thanks for commenting 👍🏻

[@SimpsonEE]

1^1/5=(𝑒^2𝜋𝑘𝑖)^1/5=𝑒^2𝜋𝑘𝑖/5=cos(2𝜋𝑘/5)+𝑖sin(2𝜋𝑘/5). Letting k=0..4 gives the same 5 answers, only in one line rather than 20 minutes of algebra. And works for any power, not just 5.