SOLUTION: x^3=2

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Question 1204813: x^3=2
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3=2
x=root%283%2C2%29=> real solution
Complex solutions:
x+=+-1%2Froot%283%2C2%29+%2B%28i%2Asqrt%283%29%29%2Froot%283%2C2%29%29
x+=+-1%2Froot%283%2C2%29+-+%28i%2Asqrt%283%29%29%2Froot%283%2C2%29%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
.

        The answer in the post by @MathLover1 is INCORRECT.

        I came to bring a correct answer. 


The real root is  root%283%2C2%29 = 1.259921...


Two other complex roots are  

    root%283%2C2%29.(cos%282pi%2F3%29+%2B+i%2Asin%282pi%2F3%29%29) = root%283%2C2%29.(-1%2F2+%2B+i%2Asqrt%283%29%2F2%29) = -root%283%2C2%29%2F2 + i%2Aroot%283%2C2%29%2A%28sqrt%283%29%2F2%29,


    root%283%2C2%29.(cos%284pi%2F3%29+%2B+i%2Asin%284pi%2F3%29%29) = root%283%2C2%29.(-1%2F2+-+i%2Asqrt%283%29%2F2%29) = -root%283%2C2%29%2F2 - i%2Aroot%283%2C2%29%2A%28sqrt%283%29%2F2%29.


ANSWER.  The three roots are  root%283%2C2%29,  -root%283%2C2%29%2F2 + i%2Aroot%283%2C2%29%2A%28sqrt%283%29%2F2%29,  -root%283%2C2%29%2F2 - i%2Aroot%283%2C2%29%2A%28sqrt%283%29%2F2%29.

Solved.