Exercise:
Bestimme die Lösungsmenge L_x der folgen quadratischen Gleichungen ohne Diskussion von Sonderfällen. nprvmulticols abclist abc x^ + ax - a abc x^ -ax + a x abc ax^ + a + b bx^ + ax + a abc x^ - x - ax+ abc x+a^ x^ + a^ + ax abc abx^ + bc-adx cd abc x-tx-t x+t+ abc dfracx^-n+ + dfracx+n+  x^ abc x^ - qtycosalpha+tanalphax + sinalpha abc qtyax+b^ + qtyax+bc c^ abclist nprvmulticols

Solution:
prvminipagecm abclist abc al x^ + ax - a &&|textMF al x_ frac-a pm sqrta^ + a L_x qtyfrac-a pm sqrta^ + a abc al x^ -ax + a x uf -x x^ -a+x + a &&|textMF al x_ fraca+ pm sqrta+^ - a fraca+ pm sqrta^ + a + -a fraca+ pm sqrta^ - a + fraca+ pm qtya- L_x qtya abc al ax^ + a + b bx^ + ax + a uf -bx^ -ax -a a-bx^ -ax + a+b &&|textMF al x_ fraca pm sqrta^ - a-ba+ba-b fraca pm sqrta^ -a^ + b^a-b fraca pm ba-b fracapm ba-b L_x qtyfraca+ba-b abc al x^ - x - ax+ tu x^ - x - ax + a uf - ax -a x^ - +ax - +a &&|textMF al x_ frac+a pm sqrt+a + a^ + +a frac+a pm sqrta^ +a + frac+a pm qtya+ L_x qtyfraca+ - abc al x+a^ x^ + a^ + ax tu x^ + x^a + xa^ + a^ x^ + a^ + ax uf -x^ -a^ -ax ax^ + aa-x tu axx+a- L_x qty-a+ abc al abx^ + bc-adx cd uf - cd abx^ + bc-adx - cd &&|textMF al x_ frac-bc-ad pm sqrtb^c^ - abcd + a^d^ + abcdab frac-bc + ad pm sqrtb^c^ + abcd + a^d^ab frac-bc + ad pm qtybc+adab L_x qtyfracdb -fracca abc al x-tx-t x+t+ tu x^-xt+t^ x + t + uf -x -t - x^-t+x + t^-t- &&|textMF al x_ fract+ pm sqrtt^+t+ - t^-t- t+ pm sqrtt^+ t + t+ pm qtyt+ L_x qtyt+ t- abc al dfracx^-n+ + dfracx+n+ x^ n+n+ x^-n+ + x+n+ x^n+n+ tu n x^ + n x + x^ + x - n^x^ + nx^ + x^ uf -n^x^-nx^-x^ -n^ x^ - n x^ + n x + x - tu n^+nx^ - n+x + &&|textMF al x_ fracn+ pm sqrtn+^ - n^+nn^+ fracn+ pm sqrtn^ + n + - n^ -nn^+ fracn+ pm n^+n fracn+ pm nn+ L_x qtyfracn fracn+ abc al x^ - qtycosalpha+tanalphax + sinalpha &&|textMF al x_ fraccosalpha+tanalpha pm sqrtcos^alpha + cosalphatanalpha + tan^alpha - sinalpha fraccosalpha + tanalpha pm sqrtcos^alpha + sinalpha + tan^alpha-sinalpha fraccosalpha + tan alpha pm sqrtcos^alpha - sinalpha + tan^alpha fraccosalpha + tanalpha pm sqrtcos^alpha -cosalphatanalpha + tan^alpha fraccosalpha + tanalpha pm qtycosalpha + tanalpha L_x qtycosalpha tanalpha abc al qtyax+b^ + qtyax+bc c^ uf z:ax+b z^ + cz c^ uf -c^ z^ + cz -c^ &&|textMF al z_ frac-c pm sqrtc^ + c^ frac-c pm c uf x:fracz-ba x_ frac-cpmc -ba L_x qtyfrac-b-ca frac-b+ca abclist prvminipage