Ekvationer

Frage	Antworten
Lös \(2x^2=72\)	\(2x^2=72\) \(x^2=36\) \(x=\pm\sqrt{36}\) \(x=\pm6\)
Lös \(3x^2+2=17\)	\(3x^2+2=17\) \(3x^2=15\) \(x^2=5\) \(x=\pm\sqrt{5}\)
Lös \(3x^2+17=2\)	\(3x^2+17=2\) \(3x^2=-15\) \(x^2=-5\) \(x=\sqrt{-5}\) Saknar reell lösning
Lös \(2x^2+12x-32=0\)	\(2x^2+12x-32=0\) \(x^2+6x-16=0\) \(x=-\frac{6}{2}\pm\sqrt{(\frac{6}{2})^2-(-16)}\) \(x=3\pm5\) \(x_1=2,x_2=-8\)
Lös \(x^2+px+q=0\)	\(x^2+px+q=0\) \(x=-\frac{p}{2}\pm\sqrt{(\frac{p}{2})^2-q}\) (OBS! Måste vara \(1\cdot x^2\))
Lös \(ab=0\)	Nollproduktmetoden \(a=0\) eller \(b=0\)
Lös \((x-2)(x+5)=0\)	Nollproduktmetoden \(x-2=0\Rightarrow x_1=2\) \(x+5=0\Rightarrow x_2=-5\)
Lös \(2x^2-4x=0\)	\(2x^2-4x=0\) \(2x(x-2)=0\) \(x_1=0\) \(x-2=0\Rightarrow x_2=2\)
Lös \(x^3-2x^2-8x=0\)	\(x^3-2x^2-8x=0\) \(x(x^2-2x-8)=0\) \(x_1=0\) \(x^2-2x-8=0\) PQ: \(x_2=4, x_3=-2\)
Lös \(x^4-8x^2-9=0\)	\(x^4-8x^2-9=0\) Substitution: \(t=x^2\) \(t^2-8t-9=0\) PQ: \(t_1=9, t_2=-1\) \(x^2=9\Rightarrow x=\pm3\) \(x^2=-1\Rightarrow Ej reella lösn\)

Zusammenfassung der Ressource

	Erstellt von Joacim Jonsson vor fast 7 Jahre