Question

calcule : (1+a elevado a um terco)(1-a elevado a um terco+a elevado a 2 sobre 3)

Answer 1

Temos que:

 

$\text{X}=\left(1+\text{a}^{\frac{1}{3}}\right)\left(1-\text{a}^{\frac{1}{3}}+\text{a}^{\frac{2}{3}}\right)$

 

Observe que:

 

$\text{a}^{\frac{1}{3}}=\sqrt[3]{\text{a}}$

 

$\text{a}^{\frac{2}{3}}=\sqrt[3]{\text{a}^2}$

 

Desta maneira, temos:

 

$\text{X}=(1+\sqrt[3]{\text{a}})(1-\sqrt[3]{\text{a}}+\sqrt[3]{\text{a}^2})$

 

$\text{X}=1+\sqrt[3]{\text{a}}+\sqrt[3]{\text{a}^2}+\sqrt[3]{\text{a}}-(\sqrt[3]{\text{a}})^2+\sqrt[3]{\text{a}^3}$

 

Donde, obtemos:

 

$\text{X}=1+\text{a}$