Exercise:
Bestimme die Lösungsmenge L_x der folgen reinquadratischen Gleichungen. nprvmulticols abclist abc x^ - abc x^ abc x^ + x^ - abc dfracx^ dfrac abc x-^ x-^ abc x-x+ x+x+ abc x^ - -x^ abc x+x- -x^ abc +x-x x+x- abc x^-^ x^ + abc x+^ + x-^ abc +x-x x+^-x+^ abclist nprvmulticols

Solution:
prvminipagecm abclist abc al x^ - uf+ x^ ufsqrt x_ pm loes- L"osungsformel: a c- alx_ pm sqrt-frac ca pm sqrt pm abc al x^ uf sqrt x_ pm loes- L"osungsformel: a c- alx_ pm sqrt-frac ca pm sqrt pm abc al x^ + x^ - uf+-x^ x^ uf: x^ ufsqrt x_ pm loes- L"osungsformel: a c- alx_ pm sqrt-frac ca pm sqrt pm abc al dfracx^ dfrac uf x^ frac frac x^ ufsqrt x_ frac loes-fracfrac L"osungsformel: a c-dfrac alx_ pm sqrt-frac ca pm sqrtfrac pm frac abc al x-^ x-^ tu x^ - x + x^ -x + uf+x-x^- x^ uf: x^ ufsqrt x_ pm loes- L"osungsformel: a c- alx_ pm sqrt-frac ca pm sqrt pm abc al x-x+ x+x+ tu x^ + x -x - x^ + x + x + tu x^ + x - x^ + x + uf-x -x^ + x^ ufsqrt x_ pmsqrt loes-sqrtsqrt L"osungsformel: a c- alx_ pm sqrt-frac ca pm sqrt abc al x^ - -x^ uf+ x^ + x^ uf: x^ ufsqrt x pm loes- abc alx+x- -x^ tu x^ - -x^ uf+ x^ + x^ uf: x^ ufsqrt x pm loes- abc al +x-x x+x- - x^ x^ - uf+ x^ + x^ uf: x^ ufsqrt pm x loes- abc al x^-^ x^ + tu x^ - x^ + x^ + uf -x^ + x^ - x^ uf: x^ ufsqrt pm x loes- abc al x+^ + x-^ tu x^ + x + + x^ - x + tu x^ + uf- x^ uf: x^ ufsqrt x pm loes- abc al +x-x x+^-x+^ tu - x^ x^ + x nonumber &quad + -x^ + x + tu - x^ x^ - uf+x^ + x^ uf: x^ ufsqrt pm x loes- abclist prvminipage