Find-the-value-of-x-x-3-64-0-Mastermind-

Question Number 168527 by Mastermind last updated on 12/Apr/22

F i n d t h e v a l u e o f x

x^{3} + 64 = 0

M a s t e r m i n d

Answered by Mathspace last updated on 12/Apr/22

x^{3} + 64 = 0 \Leftrightarrow x^{3} + 4^{3} = 0 \Leftrightarrow

(x + 4) (x^{2} - 4 x + 16) = 0 \Leftrightarrow x = - 4

o r x^{2} - 4 x + 16 = 0

Δ^{^{'}} = {(- 2)}^{2} - 16 = 4 - 16 = - 12 \Rightarrow

t h e ? r o o t s a r e z_{1} = 2 + 2 i \sqrt{3}

z_{2} = 2 - 2 i \sqrt{3}

t h e s o l u t i o n o f t h i s e q u a t i o n i s

- 4, z_{1} a n d z_{2}