[tex]f=x^4-(m-1)x^3+mx^2-(m-1)x+1\Big|:x^2,\quad \{x\neq 0\} \\ \\ f = x^2+\dfrac{1}{x^2}-(m-1)\Big(x+\dfrac{1}{x}\Big)+m\\ \\ f = \Big(x+\dfrac{1}{x}\Big)^2-2-(m-1)\Big(x+\dfrac{1}{x}\Big)+m \\ \\ f = \Big(x+\dfrac{1}{x}\Big)^2-(m-1)\Big(x+\dfrac{1}{x}\Big)+m-2[/tex]
[tex]\text{Notam }x+\dfrac{1}{x} = t,\quad t\in (-\infty, -2]\cup[2,+\infty)\\ \\ f = t^2-(m-1)t+m-2 > 0[/tex]
Doar pana aici am putut sa ajung.
De aici nu mai reusesc sa fac.
Raspunsul final trebuie sa fie m ∈ (0,4)
