miniaufgabe.js ==== 27. März 2023 bis 31. März 2023 ==== === Montag 27. März 2023 === Ausquadrieren, Resultat in NormalformminiAufgabe("#exobinomeausquadrieren1","#solbinomeausquadrieren1", [["$\\displaystyle \\left(-\\frac{4}{3}ap^{2}-\\frac{3}{5}px^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{4}{3}ap^{2}-\\frac{3}{5}px^{2}\\right)^2 = \\frac{16}{9}a^{2}p^{4}+\\frac{8}{5}ap^{3}x^{2}+\\frac{9}{25}p^{2}x^{4}$"], ["$\\displaystyle \\left(-\\frac{8}{11}k^{2}m^{2}+\\frac{11}{9}k^{2}y^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{8}{11}k^{2}m^{2}+\\frac{11}{9}k^{2}y^{2}\\right)^2 = \\frac{64}{121}k^{4}m^{4}-\\frac{16}{9}k^{4}m^{2}y^{2}+\\frac{121}{81}k^{4}y^{4}$"], ["$\\displaystyle \\left(\\frac{3}{8}e^{2}w+\\frac{10}{9}h^{2}w\\right)^2$", "$\\displaystyle \\left(\\frac{3}{8}e^{2}w+\\frac{10}{9}h^{2}w\\right)^2 = \\frac{9}{64}e^{4}w^{2}+\\frac{5}{6}e^{2}h^{2}w^{2}+\\frac{100}{81}h^{4}w^{2}$"], ["$\\displaystyle \\left(-\\frac{5}{4}d^{2}h+\\frac{3}{5}h^{2}u\\right)^2$", "$\\displaystyle \\left(-\\frac{5}{4}d^{2}h+\\frac{3}{5}h^{2}u\\right)^2 = \\frac{25}{16}d^{4}h^{2}-\\frac{3}{2}d^{2}h^{3}u+\\frac{9}{25}h^{4}u^{2}$"], ["$\\displaystyle \\left(-\\frac{3}{7}ny-\\frac{4}{3}u^{2}y\\right)^2$", "$\\displaystyle \\left(-\\frac{3}{7}ny-\\frac{4}{3}u^{2}y\\right)^2 = \\frac{8}{7}nu^{2}y^{2}+\\frac{9}{49}n^{2}y^{2}+\\frac{16}{9}u^{4}y^{2}$"], ["$\\displaystyle \\left(-\\frac{11}{3}d^{2}f^{2}-\\frac{10}{11}f^{2}h^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{11}{3}d^{2}f^{2}-\\frac{10}{11}f^{2}h^{2}\\right)^2 = \\frac{121}{9}d^{4}f^{4}+\\frac{20}{3}d^{2}f^{4}h^{2}+\\frac{100}{121}f^{4}h^{4}$"], ["$\\displaystyle \\left(-\\frac{6}{5}f^{2}u+\\frac{5}{8}m^{2}u\\right)^2$", "$\\displaystyle \\left(-\\frac{6}{5}f^{2}u+\\frac{5}{8}m^{2}u\\right)^2 = \\frac{36}{25}f^{4}u^{2}-\\frac{3}{2}f^{2}m^{2}u^{2}+\\frac{25}{64}m^{4}u^{2}$"], ["$\\displaystyle \\left(\\frac{11}{10}b^{2}e+\\frac{5}{3}b^{2}s\\right)^2$", "$\\displaystyle \\left(\\frac{11}{10}b^{2}e+\\frac{5}{3}b^{2}s\\right)^2 = \\frac{121}{100}b^{4}e^{2}+\\frac{11}{3}b^{4}es+\\frac{25}{9}b^{4}s^{2}$"], ["$\\displaystyle \\left(\\frac{3}{8}k^{2}n-\\frac{8}{11}ky^{2}\\right)^2$", "$\\displaystyle \\left(\\frac{3}{8}k^{2}n-\\frac{8}{11}ky^{2}\\right)^2 = \\frac{9}{64}k^{4}n^{2}-\\frac{6}{11}k^{3}ny^{2}+\\frac{64}{121}k^{2}y^{4}$"], ["$\\displaystyle \\left(-\\frac{4}{7}c^{2}y^{2}-\\frac{3}{4}cw\\right)^2$", "$\\displaystyle \\left(-\\frac{4}{7}c^{2}y^{2}-\\frac{3}{4}cw\\right)^2 = \\frac{6}{7}c^{3}wy^{2}+\\frac{16}{49}c^{4}y^{4}+\\frac{9}{16}c^{2}w^{2}$"], ["$\\displaystyle \\left(\\frac{4}{3}pu-\\frac{9}{10}m^{2}p^{2}\\right)^2$", "$\\displaystyle \\left(\\frac{4}{3}pu-\\frac{9}{10}m^{2}p^{2}\\right)^2 = -\\frac{12}{5}m^{2}p^{3}u+\\frac{16}{9}p^{2}u^{2}+\\frac{81}{100}m^{4}p^{4}$"], ["$\\displaystyle \\left(\\frac{5}{6}ab^{2}+\\frac{8}{5}ad\\right)^2$", "$\\displaystyle \\left(\\frac{5}{6}ab^{2}+\\frac{8}{5}ad\\right)^2 = \\frac{8}{3}a^{2}b^{2}d+\\frac{25}{36}a^{2}b^{4}+\\frac{64}{25}a^{2}d^{2}$"], ["$\\displaystyle \\left(-\\frac{3}{5}p^{2}u+\\frac{11}{6}m^{2}p^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{3}{5}p^{2}u+\\frac{11}{6}m^{2}p^{2}\\right)^2 = -\\frac{11}{5}m^{2}p^{4}u+\\frac{9}{25}p^{4}u^{2}+\\frac{121}{36}m^{4}p^{4}$"], ["$\\displaystyle \\left(-\\frac{7}{5}k^{2}u-\\frac{3}{7}uy^{2}\\right)^2$", "$\\displaystyle \\left(-\\frac{7}{5}k^{2}u-\\frac{3}{7}uy^{2}\\right)^2 = \\frac{49}{25}k^{4}u^{2}+\\frac{6}{5}k^{2}u^{2}y^{2}+\\frac{9}{49}u^{2}y^{4}$"], ["$\\displaystyle \\left(-\\frac{3}{7}bp-\\frac{7}{5}f^{2}p\\right)^2$", "$\\displaystyle \\left(-\\frac{3}{7}bp-\\frac{7}{5}f^{2}p\\right)^2 = \\frac{6}{5}bf^{2}p^{2}+\\frac{9}{49}b^{2}p^{2}+\\frac{49}{25}f^{4}p^{2}$"], ["$\\displaystyle \\left(-\\frac{11}{5}nu-\\frac{7}{11}d^{2}u\\right)^2$", "$\\displaystyle \\left(-\\frac{11}{5}nu-\\frac{7}{11}d^{2}u\\right)^2 = \\frac{14}{5}d^{2}nu^{2}+\\frac{121}{25}n^{2}u^{2}+\\frac{49}{121}d^{4}u^{2}$"], ["$\\displaystyle \\left(\\frac{5}{3}k^{2}m+\\frac{6}{7}k^{2}w^{2}\\right)^2$", "$\\displaystyle \\left(\\frac{5}{3}k^{2}m+\\frac{6}{7}k^{2}w^{2}\\right)^2 = \\frac{20}{7}k^{4}mw^{2}+\\frac{25}{9}k^{4}m^{2}+\\frac{36}{49}k^{4}w^{4}$"], ["$\\displaystyle \\left(\\frac{3}{4}a^{2}m^{2}+\\frac{11}{3}m^{2}p^{2}\\right)^2$", "$\\displaystyle \\left(\\frac{3}{4}a^{2}m^{2}+\\frac{11}{3}m^{2}p^{2}\\right)^2 = \\frac{9}{16}a^{4}m^{4}+\\frac{11}{2}a^{2}m^{4}p^{2}+\\frac{121}{9}m^{4}p^{4}$"], ["$\\displaystyle \\left(-\\frac{3}{5}an+\\frac{4}{3}ns\\right)^2$", "$\\displaystyle \\left(-\\frac{3}{5}an+\\frac{4}{3}ns\\right)^2 = \\frac{9}{25}a^{2}n^{2}-\\frac{8}{5}an^{2}s+\\frac{16}{9}n^{2}s^{2}$"], ["$\\displaystyle \\left(\\frac{3}{5}e^{2}h+\\frac{5}{4}es^{2}\\right)^2$", "$\\displaystyle \\left(\\frac{3}{5}e^{2}h+\\frac{5}{4}es^{2}\\right)^2 = \\frac{9}{25}e^{4}h^{2}+\\frac{3}{2}e^{3}hs^{2}+\\frac{25}{16}e^{2}s^{4}$"]], "
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ruby ausquadrieren.rb 1
 === Dienstag 28. März 2023 === Um welchen Term muss das Binom ergänzt werden, damit ein perfektes Quadrat der Form $A^2+2AB+B^2$ entsteht?miniAufgabe("#exobinomeausquadrieren2","#solbinomeausquadrieren2", [["$\\displaystyle \\frac{24}{7}m^{3}w^{3}+\\frac{100}{49}m^{2}w^{4}$", "Das Binom hat die Form $2ab+b^2$. Daraus folgt $b=\\frac{10}{7}mw^{2}$.
Damit ist $\\displaystyle a = \\frac{2ab}{2b} = \\frac{\\frac{24}{7}m^{3}w^{3}}{2\\cdot \\frac{10}{7}mw^{2}} = \\frac{6}{5}m^{2}w$
Es fehlt also der Term $a^2 = \\frac{36}{25}m^{4}w^{2}$"], ["$\\displaystyle \\frac{16}{9}d^{2}h^{2}+\\frac{49}{64}d^{2}h^{4}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{4}{3}dh$ und $b=\\frac{7}{8}dh^{2}$.
Es fehlt also $2ab = \\frac{7}{3}d^{2}h^{3}$"], ["$\\displaystyle \\frac{16}{9}e^{2}u^{3}+\\frac{25}{81}e^{2}u^{2}$", "Das Binom hat die Form $2ab+b^2$. Daraus folgt $b=\\frac{5}{9}eu$.
Damit ist $\\displaystyle a = \\frac{2ab}{2b} = \\frac{\\frac{16}{9}e^{2}u^{3}}{2\\cdot \\frac{5}{9}eu} = \\frac{8}{5}eu^{2}$
Es fehlt also der Term $a^2 = \\frac{64}{25}e^{2}u^{4}$"], ["$\\displaystyle \\frac{25}{144}f^{4}h^{2}+\\frac{144}{121}f^{2}h^{4}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{5}{12}f^{2}h$ und $b=\\frac{12}{11}fh^{2}$.
Es fehlt also $2ab = \\frac{10}{11}f^{3}h^{3}$"], ["$\\displaystyle \\frac{121}{81}b^{4}x^{2}+\\frac{144}{121}b^{2}x^{4}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{11}{9}b^{2}x$ und $b=\\frac{12}{11}bx^{2}$.
Es fehlt also $2ab = \\frac{8}{3}b^{3}x^{3}$"], ["$\\displaystyle \\frac{16}{25}a^{2}u^{2}+\\frac{25}{9}a^{4}u^{2}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{4}{5}au$ und $b=\\frac{5}{3}a^{2}u$.
Es fehlt also $2ab = \\frac{8}{3}a^{3}u^{2}$"], ["$\\displaystyle \\frac{49}{100}e^{2}h^{2}+\\frac{8}{5}e^{2}h^{3}$", "Das Binom hat die Form $a^2+2ab$. Daraus folgt $a=\\frac{7}{10}eh$.
Damit ist $\\displaystyle b = \\frac{2ab}{2a} = \\frac{\\frac{8}{5}e^{2}h^{3}}{2\\cdot \\frac{7}{10}eh} = \\frac{8}{7}eh^{2}$
Es fehlt also der Term $b^2 = \\frac{64}{49}e^{2}h^{4}$"], ["$\\displaystyle \\frac{9}{121}k^{2}y^{4}+\\frac{3}{4}k^{2}y^{3}$", "Das Binom hat die Form $a^2+2ab$. Daraus folgt $a=\\frac{3}{11}ky^{2}$.
Damit ist $\\displaystyle b = \\frac{2ab}{2a} = \\frac{\\frac{3}{4}k^{2}y^{3}}{2\\cdot \\frac{3}{11}ky^{2}} = \\frac{11}{8}ky$
Es fehlt also der Term $b^2 = \\frac{121}{64}k^{2}y^{2}$"], ["$\\displaystyle \\frac{121}{36}b^{4}h^{2}+\\frac{8}{3}b^{3}h^{2}$", "Das Binom hat die Form $a^2+2ab$. Daraus folgt $a=\\frac{11}{6}b^{2}h$.
Damit ist $\\displaystyle b = \\frac{2ab}{2a} = \\frac{\\frac{8}{3}b^{3}h^{2}}{2\\cdot \\frac{11}{6}b^{2}h} = \\frac{8}{11}bh$
Es fehlt also der Term $b^2 = \\frac{64}{121}b^{2}h^{2}$"], ["$\\displaystyle \\frac{16}{25}k^{4}w^{2}+\\frac{9}{16}k^{2}w^{4}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{4}{5}k^{2}w$ und $b=\\frac{3}{4}kw^{2}$.
Es fehlt also $2ab = \\frac{6}{5}k^{3}w^{3}$"], ["$\\displaystyle \\frac{25}{49}b^{4}d^{2}+\\frac{6}{7}b^{3}d^{2}$", "Das Binom hat die Form $a^2+2ab$. Daraus folgt $a=\\frac{5}{7}b^{2}d$.
Damit ist $\\displaystyle b = \\frac{2ab}{2a} = \\frac{\\frac{6}{7}b^{3}d^{2}}{2\\cdot \\frac{5}{7}b^{2}d} = \\frac{3}{5}bd$
Es fehlt also der Term $b^2 = \\frac{9}{25}b^{2}d^{2}$"], ["$\\displaystyle \\frac{6}{5}m^{3}y^{2}+\\frac{16}{25}m^{2}y^{2}$", "Das Binom hat die Form $2ab+b^2$. Daraus folgt $b=\\frac{4}{5}my$.
Damit ist $\\displaystyle a = \\frac{2ab}{2b} = \\frac{\\frac{6}{5}m^{3}y^{2}}{2\\cdot \\frac{4}{5}my} = \\frac{3}{4}m^{2}y$
Es fehlt also der Term $a^2 = \\frac{9}{16}m^{4}y^{2}$"], ["$\\displaystyle \\frac{121}{25}s^{2}w^{4}+\\frac{11}{4}s^{2}w^{3}$", "Das Binom hat die Form $a^2+2ab$. Daraus folgt $a=\\frac{11}{5}sw^{2}$.
Damit ist $\\displaystyle b = \\frac{2ab}{2a} = \\frac{\\frac{11}{4}s^{2}w^{3}}{2\\cdot \\frac{11}{5}sw^{2}} = \\frac{5}{8}sw$
Es fehlt also der Term $b^2 = \\frac{25}{64}s^{2}w^{2}$"], ["$\\displaystyle \\frac{22}{3}f^{3}m^{3}+\\frac{64}{9}f^{2}m^{4}$", "Das Binom hat die Form $2ab+b^2$. Daraus folgt $b=\\frac{8}{3}fm^{2}$.
Damit ist $\\displaystyle a = \\frac{2ab}{2b} = \\frac{\\frac{22}{3}f^{3}m^{3}}{2\\cdot \\frac{8}{3}fm^{2}} = \\frac{11}{8}f^{2}m$
Es fehlt also der Term $a^2 = \\frac{121}{64}f^{4}m^{2}$"], ["$\\displaystyle \\frac{100}{121}b^{4}x^{2}+\\frac{121}{9}b^{2}x^{4}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{10}{11}b^{2}x$ und $b=\\frac{11}{3}bx^{2}$.
Es fehlt also $2ab = \\frac{20}{3}b^{3}x^{3}$"], ["$\\displaystyle \\frac{36}{49}s^{2}x^{2}+\\frac{10}{7}s^{2}x^{3}$", "Das Binom hat die Form $a^2+2ab$. Daraus folgt $a=\\frac{6}{7}sx$.
Damit ist $\\displaystyle b = \\frac{2ab}{2a} = \\frac{\\frac{10}{7}s^{2}x^{3}}{2\\cdot \\frac{6}{7}sx} = \\frac{5}{6}sx^{2}$
Es fehlt also der Term $b^2 = \\frac{25}{36}s^{2}x^{4}$"], ["$\\displaystyle \\frac{81}{100}h^{4}k^{2}+\\frac{25}{36}h^{2}k^{2}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{9}{10}h^{2}k$ und $b=\\frac{5}{6}hk$.
Es fehlt also $2ab = \\frac{3}{2}h^{3}k^{2}$"], ["$\\displaystyle \\frac{16}{25}b^{2}n^{2}+\\frac{25}{9}b^{2}n^{4}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{4}{5}bn$ und $b=\\frac{5}{3}bn^{2}$.
Es fehlt also $2ab = \\frac{8}{3}b^{2}n^{3}$"], ["$\\displaystyle \\frac{81}{121}x^{2}y^{4}+\\frac{121}{100}x^{2}y^{2}$", "Das Binom hat die Form $a^2+b^2$. Daraus folgt $a=\\frac{9}{11}xy^{2}$ und $b=\\frac{11}{10}xy$.
Es fehlt also $2ab = \\frac{9}{5}x^{2}y^{3}$"], ["$\\displaystyle \\frac{8}{5}h^{2}x^{3}+\\frac{121}{25}h^{2}x^{4}$", "Das Binom hat die Form $2ab+b^2$. Daraus folgt $b=\\frac{11}{5}hx^{2}$.
Damit ist $\\displaystyle a = \\frac{2ab}{2b} = \\frac{\\frac{8}{5}h^{2}x^{3}}{2\\cdot \\frac{11}{5}hx^{2}} = \\frac{4}{11}hx$
Es fehlt also der Term $a^2 = \\frac{16}{121}h^{2}x^{2}$"]], "
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ruby ausquadrieren.rb 2