SOLUTION: x^6 - 511x^3-512 = 0 find all real solutions of the equation. hi, im having trouble factoring this out..getting confused with the exponents. thank you for your time!

Question 498680: x^6 - 511x^3-512 = 0
find all real solutions of the equation.
hi, im having trouble factoring this out..getting confused with the exponents.
thank you for your time!
Found 2 solutions by richard1234, Earlsdon:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We can let y = x^3, so our polynomial becomes

y^2 - 511y^2 - 512 = 0, which factors to

(y-512)(y+1) = 0

y = 512, -1 = x^3

The only real solutions are x = -1 and x = 8.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Treat this as a quadratic equation in thus:
Now factor this.
Apply the "zero product" rule:
or
Now since the original equation is a 6th order equation, we can expect 6 roots.
Here's how we get them:
This is the sum of cubes which can be factored thus:
so...
Apply the "zero product" rule:
so
Apply the quadratic formula to get:
and
For the other three roots, we have:
This is the difference of cubes which factors as:
Apply the "zero product" rule:
so
Apply the quadratic formula to get:
and
RELATED QUESTIONS
Hi. I'm having trouble finishing this equation. Can you help me? Find all real... (answered by Fombitz)
I am having trouble figuring out how to solve this problem. Find all real solutions to (answered by ikleyn)
Find all real solutions of the equation. (If there is no real solution, enter NO REAL... (answered by scott8148)
Determine all solutions of the given equation. Express in radians. 2(cosx)^2-sinx-1=0 (answered by Alan3354,lwsshak3)
Hello! I'm having trouble getting the correct answer for this problem with the... (answered by ankor@dixie-net.com)
I'm having some trouble getting the other value of "x" on this problem, Can you help me? (answered by jim_thompson5910)
find all solutions... (answered by Alan3354)
Find the real solutions of the equation by factoring:... (answered by nerdybill)
Hello! I'm having trouble getting the correct answer for this problem with the quadratic (answered by jim_thompson5910)