Please focus on the concept to solve this problem, because I can't handle to research on difficult terminology. Thanks in advance.
Find all real roots by Galois theory and find all other root to this equation: $x^8+x^6+x^4=340$
closed as unclear what you're asking by Bookend, Solid Snake, USER91500, Strants, Aloizio Macedo Oct 4 '15 at 13:34
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.
If we can solve $$u^4+u^3+u^2=340$$ then by letting $u=x^2$ we can solve the original equation. But the displayed equation is of degree 4, and there is a formula for solving those. Just search for "quartic formula".
I'm sorry that this doesn't use Galois Theory, but I don't see what Galois Thoery can do for this problem.