vault backup: 2022-03-23 09:33:19

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
         }
       ]
     }

notes/mat/Rovnice.md

@@ -90,4 +90,73 @@ $$\frac{1\pm3}{2}$$
 
 ---
 $$\frac{4\pm\sqrt{(-4)^2-4*2(-16)}}{2*2}$$
-$$\frac{4\pm\sqrt{144}}{4}$$
+$$\frac{4\pm\sqrt{144}}{4}$$
+---
+
+$$
+3x^2 - 2x + 5 = 0
+$$
+
+
+$$x_1,x_2 = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
+$$
+\frac{2\pm\sqrt{(-2)^2-4*3*5}}{2*3}
+$$
+$$
+\frac{2\pm\sqrt{-56}}{6}
+$$
+$$K=\{\emptyset\}$$
+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}