kgv ((4+2x))/3 >,x^9-3

Lösung

kgv

\frac{( 4 + 2 x )}{3} >, x^{9} - 3

\frac{4 + 2 x}{3} > (x - 93) (x^{2} + 93 x + 3^{\frac{2}{9}}) (x^{6} + 33 x^{3} + 3^{\frac{2}{3}})

Schritte zur Lösung

Finde das kleinste gemeinsame Vielfache von

\frac{( 4 + 2 x )}{3} >, x^{9} - 3

Faktorisiere

x^{9} - 3 : (x - 93) (x^{2} + 93 x + 3^{\frac{2}{9}}) (x^{6} + 33 x^{3} + 3^{\frac{2}{3}})

Multiply each factor with the highest power:

(\frac{4 + 2 x}{3}) \cdot (x - 93) \cdot (x^{2} + 93 x + 3^{\frac{2}{9}}) \cdot (x^{6} + 33 x^{3} + 3^{\frac{2}{3}})

l c m x^{2} + 2 x + 1, 3 x^{3} + x^{2} + 2 x + 5

l c m 2 + 3, (2 x + 3)

l c m \frac{4}{3} \cdot x^{2}, - \frac{1}{2} \cdot x, \frac{6}{5} \cdot x^{3}

l c m 3 a - 2 b + c, 5 a + 8 b - 7 c

l c m b, - 37 \cdot 1523 + \frac{( - 323.8 )}{7} + \frac{9}{21}