$x^9 - 2x^7 + 1 > 0$ $x^9 - 2x^7 + 1 > 0$
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.

Rewriting it as $$x^7(x^2-2)=x^7(x-\sqrt{2})(x+\sqrt{2})>-1$$ we see it holds for $-\sqrt{2}\le x\le0$ and $\require\color \color\red{x\ge \sqrt{2}}$. We can extend the former interval as $\color\red {-\sqrt{2}\le x < 1}$ noting that the LHS is decreasing in $(0,1)$ and it becomes $-1$ when $x=1$. With a similar reasoning, we could extend both our two intervals respectively further to the left and to the right, but as Emilio pointed out, only numerical approximations are effective.
