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Beliebt Algebra >

3x^{0.5}-8x^{0.25}+2=0

Lösung

3 x^{0.5} - 8 x^{0.25} + 2 = 0

Lösung

x = \frac{1316}{81} + \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}, x = \frac{1316}{81} - \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

+1

Dezimale

x = 32.48774 \dots, x = 0.00608 \dots

Schritte zur Lösung

3 x^{0.5} - 8 x^{0.25} + 2 = 0

Verwende die folgende Exponenteneigenschaft

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{0.5} = (x^{\frac{1}{4}})^{(0.5 \cdot 4)}

3 (x^{\frac{1}{4}})^{2} - 8 x^{\frac{1}{4}} + 2 = 0

Schreibe die Gleichung um mit

x^{\frac{1}{4}} = u

3 u^{2} - 8 u + 2 = 0

Löse

3 u^{2} - 8 u + 2 = 0 : u = \frac{4 + 1 0 ^{\frac{1}{2}}}{3}, u = \frac{4 - 1 0 ^{\frac{1}{2}}}{3}

u = \frac{4 + 1 0 ^{\frac{1}{2}}}{3}, u = \frac{4 - 1 0 ^{\frac{1}{2}}}{3}

Setze

u = x^{\frac{1}{4}} w i e d er e in,

löse für

x

Löse

x^{\frac{1}{4}} = \frac{4 + 1 0 ^{\frac{1}{2}}}{3} : x = \frac{1316}{81} + \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

Löse

x^{\frac{1}{4}} = \frac{4 - 1 0 ^{\frac{1}{2}}}{3} : x = \frac{1316}{81} - \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

x = \frac{1316}{81} + \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}, x = \frac{1316}{81} - \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

Überprüfe die Lösungen:

x = \frac{1316}{81} + \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

Wahr

, x = \frac{1316}{81} - \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

Wahr

Die Lösungen sind

x = \frac{1316}{81} + \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}, x = \frac{1316}{81} - \frac{416 \cdot 1 0 ^{\frac{1}{2}}}{81}

Graph

Beliebte Beispiele

x^{\frac{5}{3}} = - 243

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\frac{4 x}{9} - 3 = 7

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45 + 20 = a

30000=15000*x^{7.99}

30000 = 15000 \cdot x^{7.99}

x-sqrt(3x-14)=6

x - 3 x - 14 = 6