Lösung
löse nach x,(7x4+y)3+c=m
Lösung
x=73m−c−y,x=−73m−c−y,x=i473m−c−y,x=−i473m−c−y,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m),x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+2π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+2π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+4π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+4π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+6π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+6π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m),x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+2π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+2π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+4π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+4π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+6π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+6π
Schritte zur Lösung
(7x4+y)3+c=m
Verschiebe cauf die rechte Seite
(7x4+y)3=m−c
Für g3(x)=f(a) sind die Lösungeng(x)=3f(a),3f(a)2−1−3i,3f(a)2−1+3i
Löse 7x4+y=3m−c:x=73m−c−y,x=−73m−c−y,x=i473m−c−y,x=−i473m−c−y
Löse 7x4+y=3m−c2−1+3i:x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m),x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+2π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+2π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+4π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+4π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+6π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+6π
Löse 7x4+y=3m−c2−1−3i:x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m),x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+2π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+2π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+4π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+4π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+6π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+6π
Die Lösungen sind
x=73m−c−y,x=−73m−c−y,x=i473m−c−y,x=−i473m−c−y,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m),x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+2π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+2π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+4π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+4π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−3−c+m−2y33−c+m)+6π+i47(−c+m)32+y2+y3−c+msin4arctan(−3−c+m−2y33−c+m)+6π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m),x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+2π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+2π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+4π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+4π,x=47(−c+m)32+y2+y3−c+mcos4arctan(−−3−c+m−2y33−c+m)+6π+i47(−c+m)32+y2+y3−c+msin4arctan(−−3−c+m−2y33−c+m)+6π