ax^4+bx^2+c=0

Lösung

a x^{4} + b x^{2} + c = 0

x = \frac{- b + b ^{2} - 4 a c}{2 a}, x = - \frac{- b + b ^{2} - 4 a c}{2 a}, x = \frac{- b - b ^{2} - 4 a c}{2 a}, x = - \frac{- b - b ^{2} - 4 a c}{2 a}

Schritte zur Lösung

a x^{4} + b x^{2} + c = 0

Schreibe die Gleichung um mit

u = x^{2}

und

u^{2} = x^{4}

a u^{2} + b u + c = 0

Löse

a u^{2} + b u + c = 0 : u = \frac{- b + b ^{2} - 4 a c}{2 a}, u = \frac{- b - b ^{2} - 4 a c}{2 a}; a \neq = 0

u = \frac{- b + b ^{2} - 4 a c}{2 a}, u = \frac{- b - b ^{2} - 4 a c}{2 a}; a \neq = 0

Setze

u = x^{2} w i e d er e in,

löse für

x

Löse

x^{2} = \frac{- b + b ^{2} - 4 a c}{2 a} : x = \frac{- b + b ^{2} - 4 a c}{2 a}, x = - \frac{- b + b ^{2} - 4 a c}{2 a}

Löse

x^{2} = \frac{- b - b ^{2} - 4 a c}{2 a} : x = \frac{- b - b ^{2} - 4 a c}{2 a}, x = - \frac{- b - b ^{2} - 4 a c}{2 a}

Die Lösungen sind

x = \frac{- b + b ^{2} - 4 a c}{2 a}, x = - \frac{- b + b ^{2} - 4 a c}{2 a}, x = \frac{- b - b ^{2} - 4 a c}{2 a}, x = - \frac{- b - b ^{2} - 4 a c}{2 a}

x^{5} + 5 x^{4} - 2 x^{3} - 10 x^{2} + x + 5 = 0

(x - 3)^{4} + (x - 5)^{4} = 20

roo t s x^{3} - 6 x^{2} + 11 x - 6

10 x^{9} = 7 x

10 x^{9} - 9 x^{10} = 0.75