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Popular >

(72)/((x^{8/5))}=((x^{7/5}))/(24)

Solución

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

Solución

x = 12

Pasos de solución

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

Utilizar multiplicación cruzada (regla de tres): Si

\frac{a}{b} = \frac{c}{d}

entonces

a \cdot d = b \cdot c

72 \cdot 24 = x^{\frac{8}{5}} x^{\frac{7}{5}}

Mover

x^{\frac{8}{5}} x^{\frac{7}{5}}

al lado izquierdo

1728 - x^{\frac{8}{5}} x^{\frac{7}{5}} = 0

Factorizar

1728 - x^{\frac{8}{5}} x^{\frac{7}{5}} : - (x - 12) (x^{2} + 12 x + 144)

- (x - 12) (x^{2} + 12 x + 144) = 0

Utilizando el teorema de factor cero: si

ab = 0

entonces

a = 0

o

b = 0

x - 12 = 0 or x^{2} + 12 x + 144 = 0

Resolver

x - 12 = 0 : x = 12

Resolver

x^{2} + 12 x + 144 = 0 :

Sin solución para

x \in R

x = 12

Verificar las soluciones:

x = 12

Verdadero

La solución es

x = 12

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