[latex] x^{4} + 6 x^{2} - 27 =0[/latex]

x²=aa²+6a-27=0a1+a2=-6 u a1*a2=-27a1=-9⇒x²=-9 нет решенияa2=3⇒x²=3⇒x=-√3 u x=√3

[latex]x^4+6x^2-27=0 \ \ x^2=m geq 0\ \ m^2+6m-27=0 \ \ Delta=6^2+4*27=36+108=12^2 \ \ m_1= frac{-6-12}{2}=-9 extless 0 \ m_2= frac{-6+12}{2}=3 extgreater 0 \ \ x^2=3iff (x- sqrt{3})(x+ sqrt{3})=0 \ \ underline{x_1=- sqrt{3};x_2= sqrt{3} } [/latex]