SOLUTION: x^6-9x^3-10=0

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Question 400662: x^6-9x^3-10=0
Found 2 solutions by richard1234, sofiyac:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Let z+=+x%5E3 so that we can obtain a quadratic:

z%5E2+-+9z+-+10+=+0

%28z-10%29%28z%2B1%29+=+0

z = 10, z = -1. Since z+=+x%5E3 we have

x%5E3+=+10, x%5E3+=+-1 Each of these equations has three complex roots that form roots of unity. For the first equation, we have x+=+root%283%2C+10%29 as well as x+=+5+%2B-+5sqrt%283%29i. The second equation has roots x+=+-1 as well as x+=+1%2F2+%2B-+%28sqrt%283%29%2F2%29i.

Answer by sofiyac(983) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E6-9x%5E3-10=0
+%28x%5E3-10%29%28x%5E3%2B1%29=0++ Set each part equal to zero and solve for x
+x%5E3-10=0++ add 10 to each side
+x%5E3=10++ Take cubed root of each side
+x=cbrt%2810%29+++ *The application doesn't know how to write cubed root* but basically it's a radical sign (like a square root sign, only instead of 2 on the top left of it, you have 3
+x%5E3%2B1=0++ subtract 1 from each side
+x%5E3=-1++ take cubed root of each side
+x=-1++