Opløsninger af kubiske Ligninger. 



S3 



2(l-k)(s— kr)— 2 (2(:a+pq) + -^-f(pq)^(p + q)Cp^+q)) 

 2(1 _ k) (s - kr) - (q - kp)2 ^ -Ö>lziS!-C2(a + pq) 



.il 



+ öCpq)^ (P + q) (P^ + qh — (pq)^ (p^+q^)^J 

 2(1 - k) (s — kr) - (q - kp^) ^ 



2(1 — k)2 ^ "^ 



+ J Cpq)' (P^ + qb^ (p? + q% — 4(pq)^) 



pq 



s — kr — m;l — k) = 



1 





12^ p3 

 4(1 - k) (s - kr - m (1 — k)) = 



Cp+q)(p^+q?+(pq)"ï) 



1 (p'^-q-^ 



:>-r((p^+q'^))^ - (pqrO 



(q - kp)'^ — 4a - k) (s - kr - m Cl — k)) 



,2 2 



Cp3 — q 3) 4 



3p? 



^ (P3 _ q 3)2 



|X(q_ kpy^-4(l-k)(s-kr-m(l - k)) =— -7-f- K-3 



Cp3 - qî)! ti 2 2. 



^ ^^P' + ^')'' — 4(pq)3J 

 op3 



3p = 



n^'wK(q-kp)^ - 4(1 - k)(s-kr-m(l-k)) 



2(1 - k) 



= - -^(pq)^ (p^ -H q"^)' ^p^ - q*^ V^ 



x = - (a + pq + -g-(pq)^ (p^ + qb^ (p ^ + q?' - 4(pq)i) 



^ 4-(pq)* (p^ + ér ir ~ é^ V^s 



6 



X .= - (a + pq — ^-(Pq)-' (pi + q^^ (_ T 



1^1A=11^ 



]' 



. j-l ^ ]/_3J qt ^ 2(pq^b 



