SOLUTION: Hi everyone, I need to know how to solve this equation 8x^6+7x^3-1=0 by using the quadratic equation - though, I would also want to know how to turn this equation to a quadratic, t

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Question 17951: Hi everyone, I need to know how to solve this equation 8x^6+7x^3-1=0 by using the quadratic equation - though, I would also want to know how to turn this equation to a quadratic, thanks
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
8x^6+7x^3-1=0
Put y=x^3
Then we have
8y^2+7y-1=0
8y^2+8y-1y-1=0
8y(y+1)-1(y+1)=0
(8y-1)(y+1)=0
y=1/8 or -1
Therefore,x^3=1/8 or -1
x=1/2 or [cube root of -1]
x=1/2 or [1,%281+%2B-+sqrt%283%29i%29%2F2]

Thus we get 4 roots for the equation,
+x=%281%2F2%29
+x+=+%28-1%29
+x+=+%281+%2B-+sqrt%283%29i%29%2F2+


Hope this helps,
Prabhat