diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index c6d2680..bfdb2b2 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -13,7 +13,7 @@ { "path": "/", "date": "2022-03-23", - "size": 808686 + "size": 810665 } ], "activityHistory": [ @@ -518,7 +518,7 @@ }, { "date": "2022-03-23", - "value": 629 + "value": 2608 } ] } diff --git a/notes/mat/Rovnice.md b/notes/mat/Rovnice.md index 8f44cd7..12f9697 100644 --- a/notes/mat/Rovnice.md +++ b/notes/mat/Rovnice.md @@ -90,4 +90,73 @@ $$\frac{1\pm3}{2}$$ --- $$\frac{4\pm\sqrt{(-4)^2-4*2(-16)}}{2*2}$$ -$$\frac{4\pm\sqrt{144}}{4}$$ \ No newline at end of file +$$\frac{4\pm\sqrt{144}}{4}$$ +--- + +$$ +3x^2 - 2x + 5 = 0 +$$ + + +$$x_1,x_2 = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ +$$ +\frac{2\pm\sqrt{(-2)^2-4*3*5}}{2*3} +$$ +$$ +\frac{2\pm\sqrt{-56}}{6} +$$ +$$K=\{\emptyset\}$$ +Úloha nemá řešení, záporný discriminant + +--- +$$3x^2-2x-5=0$$ +$$D=b^2-4ac=2^2-4*3*(-5)=4+4*3*5=4+60=64$$ +$$x_1,x_2=\frac{-b\pm\sqrt{D}}{2a}=\frac{2\pm\sqrt{64}}{2*3}$$ +$$x_1,x_2=\frac{2\pm8}6$$ +$$x_1=\frac{10}6=\frac53$$ +$$x_2=\frac{-6}{6}=-1$$ +$$k=\{\frac53;-1\}$$ + +--- + +$$k=\{-1;2\}$$ + +$$(x+1)(x-2)=0$$ +$$x^2-x-2=0$$ + +--- +$$-x^2+x+2=0$$ +$$D=b^2-4ac=1^2-4*(-1)*2=1+8=9$$ +$$x_1,x_2 = \frac{-b\pm\sqrt{D}}{2a}=\frac{-1\pm3}{2*(-1)}$$ +$$\frac{-1\pm3}{-2}$$ + +--- + +$$\frac{x^2-4x-12}{x-6}=0$$ +$[x\neq6]$ + +$$x^2-4x-12=0$$ +$$D=b^2-4ac=(-4)^2-4*1*(-12)=16+48=64$$ +$$x_1,x_2=\frac{-b\pm\sqrt{D}}{2a}=\frac{-(-4)\pm\sqrt{64}}{2*1}$$ +$$\frac{4\pm8}{2}$$ +$$x_1=\frac{12}{2}=6$$ +$$x_2=\frac{-4}{2}=-2$$ +$$k=\{-2\}$$ +```ad-sentence +Nebo nebuď blbej a vykrať to +``` + +$$\frac{x^2-4x-12}{x-6}=\frac{(x-6)(x+2)}{x-6}$$ +$$x-2=0$$ +$$x=-2$$ +--- + +$$\sqrt{x-2} = x + 3$$ +$$[x > 2]$$ +$$x-2=(x+3)(x+3)$$ +$$x-2=x^2-6x+9$$ +$$x=x^2-6x+7$$ +$$0=x^2-7x+7$$ +$$D=b^2-4ac=(-7)^2-4*1*7=49-28=21$$ +$$x_1,x_2=\frac{-b\pm\sqrt{D}}{2a}=\frac{7\pm\sqrt{21}}{2*1}$$ +$$x_1=\frac{7+}{2} \ No newline at end of file