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Beliebt Algebra >

4x^66x^3=7x^3

Lösung

4 x^{6} 6 x^{3} = 7 x^{3}

Lösung

x = 0, x = - 6 \frac{7}{24}, x = 6 \frac{7}{24}, x = 0.40717 \dots + 0.70525 \dots i, x = - 0.40717 \dots - 0.70525 \dots i, x = 0.40717 \dots - 0.70525 \dots i, x = - 0.40717 \dots + 0.70525 \dots i

Schritte zur Lösung

4 x^{6} \cdot 6 x^{3} = 7 x^{3}

Verschiebe

7 x^{3}

auf die linke Seite

4 x^{6} \cdot 6 x^{3} - 7 x^{3} = 0

Faktorisiere

4 x^{6} \cdot 6 x^{3} - 7 x^{3} : x^{3} (624 x + 67) (624 x - 67) (4 \cdot 3^{\frac{2}{3}} x^{4} + 2321 x^{2} + 7^{\frac{2}{3}})

x^{3} (624 x + 67) (624 x - 67) (4 \cdot 3^{\frac{2}{3}} x^{4} + 2321 x^{2} + 7^{\frac{2}{3}}) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 624 x + 67 = 0 or 624 x - 67 = 0 or 4 \cdot 3^{\frac{2}{3}} x^{4} + 2321 x^{2} + 7^{\frac{2}{3}} = 0

Löse

624 x + 67 = 0 : x = - 6 \frac{7}{24}

Löse

624 x - 67 = 0 : x = 6 \frac{7}{24}

Löse

4 \cdot 3^{\frac{2}{3}} x^{4} + 2321 x^{2} + 7^{\frac{2}{3}} = 0 : x = 0.40717 \dots + 0.70525 \dots i, x = - 0.40717 \dots - 0.70525 \dots i, x = 0.40717 \dots - 0.70525 \dots i, x = - 0.40717 \dots + 0.70525 \dots i

Die Lösungen sind

x = 0, x = - 6 \frac{7}{24}, x = 6 \frac{7}{24}, x = 0.40717 \dots + 0.70525 \dots i, x = - 0.40717 \dots - 0.70525 \dots i, x = 0.40717 \dots - 0.70525 \dots i, x = - 0.40717 \dots + 0.70525 \dots i

Graph

Beliebte Beispiele

9 z^{4} - 3 z^{2} + 1 = 0

x^4+27x^2-324=0

x^{4} + 27 x^{2} - 324 = 0

x^4-2x^3+4x-1=0

x^{4} - 2 x^{3} + 4 x - 1 = 0

solvefor x,(x)8x^2+4y^2=12

so l v e f or x, (x) 8 x^{2} + 4 y^{2} = 12

x^{5} - 2 x = 0