Quadratisches Ergänzen
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Exercise:
Bestimme die L"osungsmenge L_x der folgen allgemeinen quadratischen Gleichungen durch quadratisches Erg"anzen. "Uberpr"ufe deine Ergebnisse mit der Mitternachtsformel. nprvmulticols abclist abc x-^ abc x^-x - abc x^-.x-. abc x^ - x - abc x^ + x abc x^ - x + abclist nprvmulticols Hinweise: .^ . ^
Solution:
prvminipagecm abclist abc al x-^ ufsqrt x- pm uf+ x pm + &&x_ x_ loes Mitternachtsformel: a b- c al x_ frac-bpm sqrtb^-aca frac pm sqrt^ - frac pm sqrt - frac pm sqrt pm abc al x^-x - qe x-^ - uf+ x-^ ufsqrt x- pm sqrt uf+ x pm sqrt + &&x_ +sqrt x_ -sqrt loes-sqrt +sqrt Mitternachtsformel: a b- c- al x_ frac-bpm sqrtb^-aca frac pm sqrt-^ - - frac pm sqrt + frac pm sqrt pm sqrt abc al x^-.x-. qe x-.^ -. uf+. x-.^ . ufsqrt x-. pm . uf+. x pm . + . &&x_. x_ -. loes-.. Mitternachtsformel: a b-. c-. al x_ frac-bpm sqrtb^-aca frac. pm sqrt-.^ - -. frac. pm sqrt. + . frac. pm sqrt . pm . abc al x^ - x - qe x-.^ -. uf+. x-.^ . ufsqrt x-. pm . uf+. x pm . + . &&x_ x_ - loes- Mitternachtsformel: a b- c- al x_ frac-bpm sqrtb^-aca frac pm sqrt-^ - - frac pm sqrt + frac pm sqrt . pm . abc al x^ + x uf: x^ + frac x frac uf-frac x^ +frac -frac qe leftx + fracright^ -frac uf+frac leftx+fracright^ frac ufsqrt x + frac pm frac uf-frac x fracpm- &&x_ frac x_ - loes-frac Mitternachtsformel: a b c- al x_ frac-bpm sqrtb^-aca frac- pm sqrt^ - - frac- pm sqrt + frac- pm sqrt frac-pm abc al x^ - x + qe x-^ - uf+ x-^ ufsqrt x- pm uf+ x pm + &&x_ x_ loes Mitternachtsformel: a b- c al x_ frac-bpm sqrtb^-aca frac pm sqrt^ - frac pm sqrt - frac pm sqrt pm abclist prvminipage
Bestimme die L"osungsmenge L_x der folgen allgemeinen quadratischen Gleichungen durch quadratisches Erg"anzen. "Uberpr"ufe deine Ergebnisse mit der Mitternachtsformel. nprvmulticols abclist abc x-^ abc x^-x - abc x^-.x-. abc x^ - x - abc x^ + x abc x^ - x + abclist nprvmulticols Hinweise: .^ . ^
Solution:
prvminipagecm abclist abc al x-^ ufsqrt x- pm uf+ x pm + &&x_ x_ loes Mitternachtsformel: a b- c al x_ frac-bpm sqrtb^-aca frac pm sqrt^ - frac pm sqrt - frac pm sqrt pm abc al x^-x - qe x-^ - uf+ x-^ ufsqrt x- pm sqrt uf+ x pm sqrt + &&x_ +sqrt x_ -sqrt loes-sqrt +sqrt Mitternachtsformel: a b- c- al x_ frac-bpm sqrtb^-aca frac pm sqrt-^ - - frac pm sqrt + frac pm sqrt pm sqrt abc al x^-.x-. qe x-.^ -. uf+. x-.^ . ufsqrt x-. pm . uf+. x pm . + . &&x_. x_ -. loes-.. Mitternachtsformel: a b-. c-. al x_ frac-bpm sqrtb^-aca frac. pm sqrt-.^ - -. frac. pm sqrt. + . frac. pm sqrt . pm . abc al x^ - x - qe x-.^ -. uf+. x-.^ . ufsqrt x-. pm . uf+. x pm . + . &&x_ x_ - loes- Mitternachtsformel: a b- c- al x_ frac-bpm sqrtb^-aca frac pm sqrt-^ - - frac pm sqrt + frac pm sqrt . pm . abc al x^ + x uf: x^ + frac x frac uf-frac x^ +frac -frac qe leftx + fracright^ -frac uf+frac leftx+fracright^ frac ufsqrt x + frac pm frac uf-frac x fracpm- &&x_ frac x_ - loes-frac Mitternachtsformel: a b c- al x_ frac-bpm sqrtb^-aca frac- pm sqrt^ - - frac- pm sqrt + frac- pm sqrt frac-pm abc al x^ - x + qe x-^ - uf+ x-^ ufsqrt x- pm uf+ x pm + &&x_ x_ loes Mitternachtsformel: a b- c al x_ frac-bpm sqrtb^-aca frac pm sqrt^ - frac pm sqrt - frac pm sqrt pm abclist prvminipage