Solving equation by radical expression

Questions
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1

This gives square and cubic radical expressions, but of complex numbers:

ToRadicals[RootReduce[ReIm[x /. Solve[x^7 == 1]]]]
2
Open in Wolfram Cloud ↗

09.nb (5.35 KB)

3

What different result are you hoping to obtain?

4

I want to solve X^13==1

5

Perhaps Mr Rachida would like to reproduce some formulas in this page: Trigonometric constants expressed in real radicals.

6

To repeat, what result are you hoping to obtain?

7

please I want to solve X^13==1 , by radical expression

8

The result from Solve has, for example, (-1)^(2/13), which is a radical.

9

please I want to solve X^13==1 , by radical expression

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10

(-1)^(2/13)

This is not a radical expression for example:

Solve[X^3 == 1]

{{X -> 1}, {X -> -(-1)^(1/3)}, {X -> (-1)^(2/3)}}

BUT,

ToRadicals[RootReduce[ReIm[X /. Solve[X^3 == 1]]]]


{{1, 0}, {-(1/2), -(Sqrt[3]/2)}, {-(1/2), Sqrt[3]/2}}
11

I found another method to solve any equation X^n==1, by radical expression.

08.nb (96 KB)