What are the real and complex solutions of the polynomial equation x^3-216=0

Question

Mathematics

Simmons

5 June, 15:23

What are the real and complex solutions of the polynomial equation x^3-216=0

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Answers (1)

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Marlee Harvey · Answer 1

A^3-b^3 = (a-b) (a^2+ab+b^2)

x^3-216=0

x^3-6^3=0

(x-6) (x^2+6x+6^2) = 0

x-6=0 or x=6

or x^2+6x+36=0

x={-6+-sqrt (6^2-4*1*36) }/2*1

={-6+-6sqrt (1-4) }/2

=-3+-sqrt (-3)

=-3+-iota sqrt 3