como faz?? nao tenho nenhuma ideia
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Simplificar ![\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\sqrt[3]{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B0%2C25%7D-%5Csqrt%5B3%5D%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D "\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\sqrt[3]{2}}")
Temos que
Logo, podemos fazer a substituição
![\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\sqrt[3]{\frac{1}{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\frac{\sqrt[3]{1}}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\frac{1}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}} \rightarrow\,\,\left(\times \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}}\right)\\ \\ =\frac{\left(\frac{1}{\sqrt[3]{2^{2}}}-\sqrt[3]{2} \right) \times \sqrt[3]{2^{2}}}{\sqrt[3]{2} \times \sqrt[3]{2^{2}}}\\ \\ =\frac{\frac{\sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}\times\sqrt[3]{2^{2}}}{\sqrt[3]{2} \times \sqrt[3]{2^{2}}}\\ \\ =\frac{1-\sqrt[3]{2^{3}}}{\sqrt[3]{2^{3}}}\\ \\ =\frac{1-2}{2}\\ \\ =\boxed{-\frac{1}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B0%2C25%7D-%5Csqrt%5B3%5D%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%5C%5C+%5C%5C+%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B2%5E%7B2%7D%7D%7D-%5Csqrt%5B3%5D%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%5C%5C+%5C%5C+%3D%5Cfrac%7B%5Cfrac%7B%5Csqrt%5B3%5D%7B1%7D%7D%7B%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D-%5Csqrt%5B3%5D%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D%5C%5C+%5C%5C+%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D-%5Csqrt%5B3%5D%7B2%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D%7D+%5Crightarrow%5C%2C%5C%2C%5Cleft%28%5Ctimes+%5Cfrac%7B%5Csqrt%5B3%5D%7B2%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B2%5E2%7D%7D%5Cright%29%5C%5C+%5C%5C+%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D-%5Csqrt%5B3%5D%7B2%7D+%5Cright%29+%5Ctimes+%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D+%5Ctimes+%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D%5C%5C+%5C%5C+%3D%5Cfrac%7B%5Cfrac%7B%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D%7B%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D-%5Csqrt%5B3%5D%7B2%7D%5Ctimes%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D%7B%5Csqrt%5B3%5D%7B2%7D+%5Ctimes+%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%7D%5C%5C+%5C%5C+%3D%5Cfrac%7B1-%5Csqrt%5B3%5D%7B2%5E%7B3%7D%7D%7D%7B%5Csqrt%5B3%5D%7B2%5E%7B3%7D%7D%7D%5C%5C+%5C%5C+%3D%5Cfrac%7B1-2%7D%7B2%7D%5C%5C+%5C%5C+%3D%5Cboxed%7B-%5Cfrac%7B1%7D%7B2%7D%7D "\frac{\sqrt[3]{0,25}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\sqrt[3]{\frac{1}{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\frac{\sqrt[3]{1}}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}}\\ \\ =\frac{\frac{1}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}}{\sqrt[3]{2}} \rightarrow\,\,\left(\times \frac{\sqrt[3]{2^2}}{\sqrt[3]{2^2}}\right)\\ \\ =\frac{\left(\frac{1}{\sqrt[3]{2^{2}}}-\sqrt[3]{2} \right) \times \sqrt[3]{2^{2}}}{\sqrt[3]{2} \times \sqrt[3]{2^{2}}}\\ \\ =\frac{\frac{\sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}}-\sqrt[3]{2}\times\sqrt[3]{2^{2}}}{\sqrt[3]{2} \times \sqrt[3]{2^{2}}}\\ \\ =\frac{1-\sqrt[3]{2^{3}}}{\sqrt[3]{2^{3}}}\\ \\ =\frac{1-2}{2}\\ \\ =\boxed{-\frac{1}{2}}")
Temos que
Logo, podemos fazer a substituição
edgar11braga:
eu só n entendi a etapa que vc fez para isolar o raiz cubica de dois (com uma seta)
pode me explicar essa parte??
tem um erro na resolução. estou corrigindo
ah ok abrigado
pronto. está corrigido agora
a etapa que você falou eu multipliquei o numerador e o denominador pela raiz cúbica de (2²). Fazendo isso, o valor da expressão não se altera
ah entendi, obrigado
Não há de quê!
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