Question

Se a = $3 + \sqrt[3]{2}$ e b = $3 - \sqrt[3]{2}$ então, o valor de (a-b)³ será: 

a) $3 \sqrt{2}$

b) $16$

c) $18 \sqrt{2}$

d) $4 \sqrt{2}$

e) $8 \sqrt{2}$

Answer 1

(a-b)^2=[3+ \sqrt[3]{2} - (3- \sqrt[3]{2})]^3= \\ \\ \ [3+ \sqrt[3]{2}-3+ \sqrt[3]{2}]^3= \\ \\ \boxed{\ [2 \sqrt[3]{2}]^3 = 16 }[/tex]