Question

,,rezolvati in R ecuatia 6x la puterea 4-5x la puterea 2+1=0

Answer 1

[tex]6x^4-5x^2+1=0\\ \text{Notam:} x^2=t\ \textgreater \ 0\\ 6t^2-5t+1=0\\ \Delta=25-4\cdot6= 1\Rightarrow \sqrt{\Delta}=1\\ t_1=\dfrac{5+1}{12}=\dfrac{1}{2}\\ t_2=\dfrac{5-1}{12}=\dfrac{1}{3}\\ x^2=\dfrac{1}{2}\Rightarrow x\in \left\{\pm \dfrac{\sqrt{2}}{2}\right\}\\ x^2=\dfrac{1}{3}\Rightarrow x\in \left\{\pm \dfrac{\sqrt{3}}{3}\right\}\\ S:x\in \left\{ \pm \dfrac{\sqrt{3}}{3};\pm \dfrac{\sqrt{2}}{2}\right\}[/tex]