Question 169
Determine the real numbers $x \gt 1$ for which there exists a triangle whose sides have lengths
$$
x^{4}+x^{3}+2 x^{2}+x+1, \quad 2 x^{3}+x^{2}+2 x+1, \quad x^{4}-1
$$
$$
x^{4}+x^{3}+2 x^{2}+x+1, \quad 2 x^{3}+x^{2}+2 x+1, \quad x^{4}-1
$$