SOLUTION: 5x^6 – 8x^3 = 4

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Question 1089503: 5x^6 – 8x^3 = 4
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Introduce new variable y = x^3. Then your equation takes the form

5y^2 - 8y = 4.


5y^2 - 8y - 4 = 0,


y%5B1%2C2%5D = %288+%2B-+sqrt%288%5E2+-4%2A5%2A%28-4%29%29%29%2F%282%2A5%29 = %288+%2B-+sqrt%28144%29%29%2F10 = %288+%2B-+12%29%2F10.


1.  y%5B1%5D = %288%2B12%29%2F10 = 2  ====>  x^3 = 2  ====>  x = root%283%2C2%29.


2.  y%5B2%5D = %288-12%29%2F10 = -0.4  ====>   x^3 = -0.4  ====>  x = -root%283%2C0.4%29.

Solved.