$x^9 - 2x^7 + 1 > 0$ $x^9 - 2x^7 + 1 > 0$
Solve in real numbers. 
How would I do this without a graphing calculator or any graphing application? I only see a $(x-1)$ root and nothing else, can't really factor an eighth degree polynomial ...
Thanks.

Hint:
You know that:$ x^9-2x^7+1=(x-1)(x^8+x^7-x^6-x^5-x^4-x^3-x^2+x-1)$.
Note that the second factor is positive for $x\rightarrow \pm \infty$, and is $-1$ for $x=0$ so it has at least two real roots.
You can use the Sturm theorem to find how many real roots has $x^8+x^7-x^6-x^5-x^4-x^3-x^2+x-1$, but it is very laborious, and don't gives the value of the roots. 
A numerical calculus show that it has really only two roots $x \sim 1.38$ and $x \sim -1.44$.
