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Popular >

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

Solución

x^{\frac{1}{3}} + 2 x^{\frac{2}{3}} - x = 0

Solución

x = 0, x = 7 + 5 \cdot 2^{\frac{1}{2}}, x = 7 - 5 \cdot 2^{\frac{1}{2}}

+1

Notación decimal

x = 0, x = 14.07106 \dots, x = - 0.07106 \dots

Pasos de solución

x^{\frac{1}{3}} + 2 x^{\frac{2}{3}} - x = 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}

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

Re escribir la ecuación con

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

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

Resolver

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

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

Sustituir hacia atrás la

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

resolver para

x

Resolver

x^{\frac{1}{3}} = 0 : x = 0

Resolver

x^{\frac{1}{3}} = 1 + 2^{\frac{1}{2}} : x = 7 + 5 \cdot 2^{\frac{1}{2}}

Resolver

x^{\frac{1}{3}} = 1 - 2^{\frac{1}{2}} : x = 7 - 5 \cdot 2^{\frac{1}{2}}

x = 0, x = 7 + 5 \cdot 2^{\frac{1}{2}}, x = 7 - 5 \cdot 2^{\frac{1}{2}}

Verificar las soluciones:

x = 0

Verdadero

, x = 7 + 5 \cdot 2^{\frac{1}{2}}

Verdadero

, x = 7 - 5 \cdot 2^{\frac{1}{2}}

Verdadero

Las soluciones son

x = 0, x = 7 + 5 \cdot 2^{\frac{1}{2}}, x = 7 - 5 \cdot 2^{\frac{1}{2}}

Ejemplos populares

3 x - 4 = 12

((2x+1))/((sqrt(4x^2-5)))=-1

\frac{( 2 x + 1 )}{( 4 x ^{2} - 5 )} = - 1

sqrt(2x-1)=sqrt(3)

2 x - 1 = 3

sqrt(2x-2)=((x+7))/4

2 x - 2 = \frac{( x + 7 )}{4}

solvefor x,sqrt(x/y)+sqrt(y/x)= 10/3 resolver para

x, \frac{x}{y} + \frac{y}{x} = \frac{10}{3}