SOLUTION: Find all real solutions x^6+7x^3-8=0

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Question 346530: Find all real solutions
x^6+7x^3-8=0
Answer by solver91311(24713) About Me  (Show Source):
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This one needs a convenient substitution. Let





Factors:



Hence



and





Factor the sum of two cubes:



So



or



Use the quadratic formula:





Summarizing so far we have three roots: but only one of them is real.

Now all you have left to do is to solve by factoring the difference of two cubes and then applying the quadratic formula to the quadratic factor and taking the real root directly from the linear factor. Sum and Difference of Cubes Discard any complex roots.


John

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