[tex]4x^4+2x^2-6=0\implies4\left(x^2\right)^2+2x^2-6=0[/tex]
Notam [tex]x^2=t[/tex]
Atunci avem: [tex]4t^2+2t-6=0[/tex]
[tex]\Delta=2^2-4\times4\times(-6)=4+96=100[/tex]
[tex]t_1=\cfrac{-2+\sqrt{100}}{2\times4}=\cfrac{-2+10}{8}=1[/tex]
[tex]\implies x^2=1\implies \boxed{x=\pm1}[/tex]
[tex]t_2=\cfrac{-2-\sqrt{100}}{2\times4}=\cfrac{-12}{8}=-\cfrac{3}{2}[/tex]
[tex]\implies x^2=-\cfrac{3}{2}[/tex], dar [tex]x^2 > 0[/tex], deci aici nu avem solutii
Inseamna ca singurele solutii sunt [tex]1[/tex], respectiv [tex]-1[/tex].
[tex]\cfrac{sin(x)}{cos(x)}=1\implies sin(x)=cos(x)[/tex]
Dar [tex]x\in(0, \ \cfrac{\pi}{2})[/tex], deci singura solutie este [tex]\boxed{x=\cfrac{\pi}{4}}[/tex]
