Question

(∛5 + ∛17) x (∛25 - ∛5 x 17 + ∛17²)

Answer 1

$( \sqrt[3]{5} +\sqrt[3]{17} )(\sqrt[3]{25}-17\sqrt[3]{5} +\sqrt[3]{17^2} )\\( \sqrt[3]{5} +\sqrt[3]{17} )( \sqrt[3]{25}-17\sqrt[3]{5}+\sqrt[3]{289})=\sqrt[3]{5}.\sqrt[3]{25} -17 \sqrt[3]{5}.\sqrt[3]{5} +\sqrt[3]{289}.\sqrt[3]{5} \\+\sqrt[3]{17}.\sqrt[3]{25}-17\sqrt[3]{5}.\sqrt[3]{17}+\sqrt[3]{17}.\sqrt[3]{289}\\=\sqrt[3]{125}-17\sqrt[3]{25}+\sqrt[3]{1445} +\sqrt[3]{425}-17\sqrt[3]{85}+\sqrt[3]{4913}\\=\boxed{5-17\sqrt[3]{25}+\sqrt[3]{1445}+\sqrt[3]{425}-17\sqrt[3]{85}+\sqrt[3]{4913}}$

Answer 2

Chamando raiz cúbica de 5 de 'a' 3 e raiz cúbica de 17 de b temos:
(a+b)(a^2-ab+b^2)
a^3 - a^2b+ ab^2 + a^2b - ab^2 + b^3
Vai sobrar a^3 + b^3= raiz cúbica de 5 elevado ao cubico + raiz cúbica de 17 elevado ao cubo
Logo 5 mais 17 igual a 22