Question

Find all the roots of the equation

`{x}^(6) - 64 = 0`
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Answer 1

x = 2

x =-2

x =1 +√3i

x =1 -√3i

x =-1 +√3i

x =-1 -√3i

Explanation:

`x^(6) -64 = 0\\(x^(3) -8)(x^(3) + 8) = 0\\ \\( x - 2) (x^(2) + 2x + 4)( x + 2) (x^(2) -2x + 4) = 0\\`

x = 2

x =-2

x =1 +√3i

x =1 -√3i

x =-1 +√3i

x =-1 -√3i

Answer 2

Standard form:
X^2 -64=0
Factorization:
(x+8)(x-8)=0

Solution:
X+8=0 x^1=-8
X-7=0. X^2=8