Solve x^6-26x^3-27

Question

Nothingoon third

Answer 1

x⁶-26x³-27=(x³-27)(x³+1), so x³=27, x=3 (plus two complex roots), or x³=1, x=1 (plus two complex roots)

COMPLEX ROOTS

x³-27=(x-3)(x²+3x+9)⇒x=(-3±√(9-36))/2=(-3±3i√3)/2;

x³-1=(x-1)(x²+x+1)⇒x=(-1±√(1-4))/2=(-1±i√3)/2.

FULL SOLUTION (6 roots)

x=1, 3, (-1+i√3)/2, (-1-i√3)/2, (-3+3i√3)/2, (-3-3i√3)/2.