miniaufgabe.js
==== 3. April 2023 bis 7. April 2023 ====
=== Montag 3. April 2023 ===
Fehler in den Lösungen, Ausfall der Miniaufgaben.
=== Dienstag 4. April 2023 ===
Keine Miniaufgabe, Prüfung (am Morgen im H21), Informatik am Nachmittag im E21.
==== 24. April 2023 bis 28. April 2023 ====
=== Montag 24. April 2023 ===
Lösen Sie folgende quadratische Gleichung (von Vorteil mit Hilfe der Mitternachtsformel):miniAufgabe("#exoquadratischegleichungen1","#solquadratischegleichungen1",
[["$4x^{2}-12x+5 = 0$", "$a=4$, $b=-12$, $c=5$
\nDiskriminante $D = b^2-4ac = \\left(-12\\right)^{2}-4 \\cdot 4 \\cdot 5 = 144-80 = 64$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 8$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-12\\right)+8}{2 \\cdot 4} = \\frac{20}{8} = \\frac{5}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-12\\right)-8}{2 \\cdot 4} = \\frac{4}{8} = \\frac{1}{2}$."], ["$6x^{2}-5x-6 = 0$", "$a=6$, $b=-5$, $c=-6$
\nDiskriminante $D = b^2-4ac = \\left(-5\\right)^{2}-4 \\cdot 6\\left(-6\\right) = 25+144 = 169$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 13$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-5\\right)+13}{2 \\cdot 6} = \\frac{18}{12} = \\frac{3}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-5\\right)-13}{2 \\cdot 6} = \\frac{-8}{12} = -\\frac{2}{3}$."], ["$8x^{2}-2x-3 = 0$", "$a=8$, $b=-2$, $c=-3$
\nDiskriminante $D = b^2-4ac = \\left(-2\\right)^{2}-4 \\cdot 8\\left(-3\\right) = 4+96 = 100$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 10$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-2\\right)+10}{2 \\cdot 8} = \\frac{12}{16} = \\frac{3}{4}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-2\\right)-10}{2 \\cdot 8} = \\frac{-8}{16} = -\\frac{1}{2}$."], ["$4x^{2}-16x+15 = 0$", "$a=4$, $b=-16$, $c=15$
\nDiskriminante $D = b^2-4ac = \\left(-16\\right)^{2}-4 \\cdot 4 \\cdot 15 = 256-240 = 16$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 4$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-16\\right)+4}{2 \\cdot 4} = \\frac{20}{8} = \\frac{5}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-16\\right)-4}{2 \\cdot 4} = \\frac{12}{8} = \\frac{3}{2}$."], ["$4x^{2}-8x+3 = 0$", "$a=4$, $b=-8$, $c=3$
\nDiskriminante $D = b^2-4ac = \\left(-8\\right)^{2}-4 \\cdot 4 \\cdot 3 = 64-48 = 16$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 4$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-8\\right)+4}{2 \\cdot 4} = \\frac{12}{8} = \\frac{3}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-8\\right)-4}{2 \\cdot 4} = \\frac{4}{8} = \\frac{1}{2}$."], ["$4x^{2}+4x-15 = 0$", "$a=4$, $b=4$, $c=-15$
\nDiskriminante $D = b^2-4ac = 4^{2}-4 \\cdot 4\\left(-15\\right) = 16+240 = 256$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 16$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-4+16}{2 \\cdot 4} = \\frac{12}{8} = \\frac{3}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-4-16}{2 \\cdot 4} = \\frac{-20}{8} = -\\frac{5}{2}$."], ["$4x^{2}+8x-5 = 0$", "$a=4$, $b=8$, $c=-5$
\nDiskriminante $D = b^2-4ac = 8^{2}-4 \\cdot 4\\left(-5\\right) = 64+80 = 144$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 12$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-8+12}{2 \\cdot 4} = \\frac{4}{8} = \\frac{1}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-8-12}{2 \\cdot 4} = \\frac{-20}{8} = -\\frac{5}{2}$."], ["$8x^{2}+2x-3 = 0$", "$a=8$, $b=2$, $c=-3$
\nDiskriminante $D = b^2-4ac = 2^{2}-4 \\cdot 8\\left(-3\\right) = 4+96 = 100$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 10$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-2+10}{2 \\cdot 8} = \\frac{8}{16} = \\frac{1}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-2-10}{2 \\cdot 8} = \\frac{-12}{16} = -\\frac{3}{4}$."], ["$4x^{2}-12x+5 = 0$", "$a=4$, $b=-12$, $c=5$
\nDiskriminante $D = b^2-4ac = \\left(-12\\right)^{2}-4 \\cdot 4 \\cdot 5 = 144-80 = 64$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 8$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-12\\right)+8}{2 \\cdot 4} = \\frac{20}{8} = \\frac{5}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-12\\right)-8}{2 \\cdot 4} = \\frac{4}{8} = \\frac{1}{2}$."], ["$6x^{2}-13x+6 = 0$", "$a=6$, $b=-13$, $c=6$
\nDiskriminante $D = b^2-4ac = \\left(-13\\right)^{2}-4 \\cdot 6 \\cdot 6 = 169-144 = 25$. Positiv, es gibt also 2 Lösungen. $\\sqrt{D} = 5$
$x_1 = \\frac{-b + \\sqrt{D}}{2a} = \\frac{-\\left(-13\\right)+5}{2 \\cdot 6} = \\frac{18}{12} = \\frac{3}{2}$ und
$x_2 = \\frac{-b - \\sqrt{D}}{2a} = \\frac{-\\left(-13\\right)-5}{2 \\cdot 6} = \\frac{8}{12} = \\frac{2}{3}$."]],
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ruby quadratische-gleichungen.rb 1
=== Dienstag 25. April 2023 ===
Ausquadrieren, zusammenfassen.miniAufgabe("#exoausquadrieren_zusammenfassen1","#solausquadrieren_zusammenfassen1",
[["$\\left(-9x+\\sqrt{7}\\right)^{2}-\\left(-10x-\\sqrt{7}\\right)^{2}$", "$\\left(-9x+\\sqrt{7}\\right)^{2}-\\left(-10x-\\sqrt{7}\\right)^{2} = 81 \\cdot x^{2}+2\\left(-9\\right) \\cdot \\sqrt{7}x+7-\\left(100 \\cdot x^{2}-2\\left(-10\\right) \\cdot \\sqrt{7}x+7\\right) = 81 \\cdot x^{2}-18 \\cdot \\sqrt{7}x+7-100 \\cdot x^{2}-20 \\cdot \\sqrt{7}x-7 = -19 \\cdot x^{2}-38 \\cdot \\sqrt{7}x$"], ["$\\left(-7x+\\sqrt{6}\\right)^{2}-\\left(-5x-\\sqrt{6}\\right)^{2}$", "$\\left(-7x+\\sqrt{6}\\right)^{2}-\\left(-5x-\\sqrt{6}\\right)^{2} = 49 \\cdot x^{2}+2\\left(-7\\right) \\cdot \\sqrt{6}x+6-\\left(25 \\cdot x^{2}-2\\left(-5\\right) \\cdot \\sqrt{6}x+6\\right) = 49 \\cdot x^{2}-14 \\cdot \\sqrt{6}x+6-25 \\cdot x^{2}-10 \\cdot \\sqrt{6}x-6 = 24 \\cdot x^{2}-24 \\cdot \\sqrt{6}x$"], ["$\\left(8x+\\sqrt{8}\\right)^{2}-\\left(5x-\\sqrt{8}\\right)^{2}$", "$\\left(8x+\\sqrt{8}\\right)^{2}-\\left(5x-\\sqrt{8}\\right)^{2} = 64 \\cdot x^{2}+2 \\cdot 8 \\cdot \\sqrt{8}x+8-\\left(25 \\cdot x^{2}-2 \\cdot 5 \\cdot \\sqrt{8}x+8\\right) = 64 \\cdot x^{2}+16 \\cdot \\sqrt{8}x+8-25 \\cdot x^{2}+10 \\cdot \\sqrt{8}x-8 = 39 \\cdot x^{2}+26 \\cdot \\sqrt{8}x$"], ["$\\left(-6x+\\sqrt{7}\\right)^{2}-\\left(7x-\\sqrt{7}\\right)^{2}$", "$\\left(-6x+\\sqrt{7}\\right)^{2}-\\left(7x-\\sqrt{7}\\right)^{2} = 36 \\cdot x^{2}+2\\left(-6\\right) \\cdot \\sqrt{7}x+7-\\left(49 \\cdot x^{2}-2 \\cdot 7 \\cdot \\sqrt{7}x+7\\right) = 36 \\cdot x^{2}-12 \\cdot \\sqrt{7}x+7-49 \\cdot x^{2}+14 \\cdot \\sqrt{7}x-7 = -13 \\cdot x^{2}+2 \\cdot \\sqrt{7}x$"], ["$\\left(-6x+\\sqrt{6}\\right)^{2}-\\left(10x-\\sqrt{6}\\right)^{2}$", "$\\left(-6x+\\sqrt{6}\\right)^{2}-\\left(10x-\\sqrt{6}\\right)^{2} = 36 \\cdot x^{2}+2\\left(-6\\right) \\cdot \\sqrt{6}x+6-\\left(100 \\cdot x^{2}-2 \\cdot 10 \\cdot \\sqrt{6}x+6\\right) = 36 \\cdot x^{2}-12 \\cdot \\sqrt{6}x+6-100 \\cdot x^{2}+20 \\cdot \\sqrt{6}x-6 = -64 \\cdot x^{2}+8 \\cdot \\sqrt{6}x$"], ["$\\left(10x+\\sqrt{7}\\right)^{2}-\\left(7x-\\sqrt{7}\\right)^{2}$", "$\\left(10x+\\sqrt{7}\\right)^{2}-\\left(7x-\\sqrt{7}\\right)^{2} = 100 \\cdot x^{2}+2 \\cdot 10 \\cdot \\sqrt{7}x+7-\\left(49 \\cdot x^{2}-2 \\cdot 7 \\cdot \\sqrt{7}x+7\\right) = 100 \\cdot x^{2}+20 \\cdot \\sqrt{7}x+7-49 \\cdot x^{2}+14 \\cdot \\sqrt{7}x-7 = 51 \\cdot x^{2}+34 \\cdot \\sqrt{7}x$"], ["$\\left(5x+\\sqrt{11}\\right)^{2}-\\left(11x-\\sqrt{11}\\right)^{2}$", "$\\left(5x+\\sqrt{11}\\right)^{2}-\\left(11x-\\sqrt{11}\\right)^{2} = 25 \\cdot x^{2}+2 \\cdot 5 \\cdot \\sqrt{11}x+11-\\left(121 \\cdot x^{2}-2 \\cdot 11 \\cdot \\sqrt{11}x+11\\right) = 25 \\cdot x^{2}+10 \\cdot \\sqrt{11}x+11-121 \\cdot x^{2}+22 \\cdot \\sqrt{11}x-11 = -96 \\cdot x^{2}+32 \\cdot \\sqrt{11}x$"], ["$\\left(-10x+\\sqrt{11}\\right)^{2}-\\left(-7x-\\sqrt{11}\\right)^{2}$", "$\\left(-10x+\\sqrt{11}\\right)^{2}-\\left(-7x-\\sqrt{11}\\right)^{2} = 100 \\cdot x^{2}+2\\left(-10\\right) \\cdot \\sqrt{11}x+11-\\left(49 \\cdot x^{2}-2\\left(-7\\right) \\cdot \\sqrt{11}x+11\\right) = 100 \\cdot x^{2}-20 \\cdot \\sqrt{11}x+11-49 \\cdot x^{2}-14 \\cdot \\sqrt{11}x-11 = 51 \\cdot x^{2}-34 \\cdot \\sqrt{11}x$"], ["$\\left(-9x+\\sqrt{10}\\right)^{2}-\\left(5x-\\sqrt{10}\\right)^{2}$", "$\\left(-9x+\\sqrt{10}\\right)^{2}-\\left(5x-\\sqrt{10}\\right)^{2} = 81 \\cdot x^{2}+2\\left(-9\\right) \\cdot \\sqrt{10}x+10-\\left(25 \\cdot x^{2}-2 \\cdot 5 \\cdot \\sqrt{10}x+10\\right) = 81 \\cdot x^{2}-18 \\cdot \\sqrt{10}x+10-25 \\cdot x^{2}+10 \\cdot \\sqrt{10}x-10 = 56 \\cdot x^{2}-8 \\cdot \\sqrt{10}x$"], ["$\\left(6x+\\sqrt{11}\\right)^{2}-\\left(-8x-\\sqrt{11}\\right)^{2}$", "$\\left(6x+\\sqrt{11}\\right)^{2}-\\left(-8x-\\sqrt{11}\\right)^{2} = 36 \\cdot x^{2}+2 \\cdot 6 \\cdot \\sqrt{11}x+11-\\left(64 \\cdot x^{2}-2\\left(-8\\right) \\cdot \\sqrt{11}x+11\\right) = 36 \\cdot x^{2}+12 \\cdot \\sqrt{11}x+11-64 \\cdot x^{2}-16 \\cdot \\sqrt{11}x-11 = -28 \\cdot x^{2}-4 \\cdot \\sqrt{11}x$"]],
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ruby ausquadrieren-zusammenfassen.rb 1