Question

Galera, ajudem-me nesta expressao
∛3 .(∛9 - 2∛3) +5) - ∛9 (∛3 + 2∛9) -2)

Answer 1

(∛3 .(∛9 - 2∛3) + 5) - (∛9 (∛3 + 2∛9) -2) =
$[3^{1/3} ( 3^{2/3} - 2(3^{1/3})) + 5] - [3^{2/3} (3^{1/3} + 2(3^{2/3})) - 2] =$
$[3^{1/3+2/3} - 2(3^{1/3+1/3}) + 5] - [3^{2/3+1/3} + 2(3^{2/3+2/3}) - 2] =$
$[3^{3/3} - 2(3^{2/3}) + 5] - [3^{3/3} + 2(3^{4/3}) - 2] =$
$[3 - 2(3^{2/3}) + 5] - [3 + 2(3^{3/3+1/3}) - 2] =$
$[8 - 2(3^{2/3})] - [1 + 2(3^{3/3}+3^{1/3})] =$
$(8 - 2 \sqrt[3]{9}) - [1 + 2(3+ \sqrt[3]{3})] =$
$(8 - 2 \sqrt[3]{9}) - 1 - 6 - 2\sqrt[3]{3} =$
$8 - 7 - 2\sqrt[3]{3} - 2 \sqrt[3]{9} =$
$1 - 2(\sqrt[3]{3} + \sqrt[3]{9}) =$
$1 - 2\sqrt[3]{3}( 1 + \sqrt[3]{3})$

ou

$8 - 2(3^{2/3}) - 1 - 2(3^{4/3}) =$
$7 - 2\sqrt[3]{9} - 2\sqrt[3]{81} =$
$7 - 2(\sqrt[3]{9} + \sqrt[3]{81})$