Proving that $x^{16} > 5$ when given a polynomial of degree $15$. I am unable to prove the following

If $x^{15}-x^{13}+x^{11}-x^9+x^7-x^5+x^3-x = 7$ prove that $x^{16} > 15$.


$ x^{14} - x^{12} + \ldots + x^2 -1 = \frac{7}{x}, $ I am considering $ x \neq 0 $ multiply both side by $ x^2 $ and add you get $ x^{16} = 1+ 7x + \frac{7}{x}. $ Take minimum of R.H.S.
