4x^{2/3}+21x^{1/3}+27=0

Solución

4 x^{\frac{2}{3}} + 21 x^{\frac{1}{3}} + 27 = 0

x = - \frac{729}{64}, x = - 27

Pasos de solución

4 x^{\frac{2}{3}} + 21 x^{\frac{1}{3}} + 27 = 0

Usar la siguiente propiedad de los exponentes

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

x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

4 (x^{\frac{1}{3}})^{2} + 21 x^{\frac{1}{3}} + 27 = 0

Re escribir la ecuación con

x^{\frac{1}{3}} = u

4 u^{2} + 21 u + 27 = 0

Resolver

4 u^{2} + 21 u + 27 = 0 : u = - \frac{9}{4}, u = - 3

u = - \frac{9}{4}, u = - 3

Sustituir hacia atrás la

u = x^{\frac{1}{3}},

resolver para

x

Resolver

x^{\frac{1}{3}} = - \frac{9}{4} : x = - \frac{729}{64}

Resolver

x^{\frac{1}{3}} = - 3 : x = - 27

x = - \frac{729}{64}, x = - 27

Verificar las soluciones:

x = - \frac{729}{64}

Verdadero

, x = - 27

Verdadero

Las soluciones son

x = - \frac{729}{64}, x = - 27

x + 2 + x - 7 = 9

x, r + s - 2 t = 2 x + y

\frac{1}{( 1 + x ^{2} )} = \frac{1}{( 2 )}

4 x^{3} - 3 x^{2.5} - 3 x + 9 = 15

x + x^{\frac{1}{2}} = 20