6-3-3-1-3-9-1-3-simplify-

Question Number 59812 by ANTARES VY last updated on 15/May/19

\frac{6}{3 + \sqrt[3]{3} + \sqrt[3]{9}} simplify .

Commented by Kunal12588 last updated on 15/May/19

l e t \sqrt[3]{3} = a

\Rightarrow \sqrt[3]{9} = a^{2}

\Rightarrow 3 = a^{3}

a + a^{2} + a^{3} = \frac{a (a^{3} - 1)}{a - 1} [s u m o f G P]

\frac{6}{3 + \sqrt[3]{3} + \sqrt[3]{9}}

= \frac{2 a^{3}}{\frac{a (a^{3} - 1)}{a - 1}} = \frac{2 a^{2} (a - 1)}{(a^{3} - 1)} = \frac{2 (a^{3} - a^{2})}{a^{3} - 1}

= \frac{2 (3 - \sqrt[3]{9})}{3 - 1} = 3 - \sqrt[3]{9}

Answered by Kunal12588 last updated on 15/May/19

S = \sqrt[3]{3} + \sqrt[3]{9} + 3

S (\sqrt[3]{3}) = \sqrt[3]{9} + 3 + 3 \sqrt[3]{3}

\Rightarrow S = \frac{\sqrt[3]{3} - 3 \sqrt[3]{3}}{(1 - \sqrt[3]{3})} = \frac{\sqrt[3]{3} (3 - 1)}{\sqrt[3]{3} - 1} = \frac{2 \sqrt[3]{3}}{\sqrt[3]{3} - 1}

\frac{6}{3 + \sqrt[3]{3} + \sqrt[3]{9}} = \frac{6}{\frac{2 \sqrt[3]{3}}{\sqrt[3]{3} - 1}} = \frac{6 (\sqrt[3]{3} - 1)}{2 \sqrt[3]{3}} = \sqrt[3]{9} (\sqrt[3]{3} - 1)

\frac{6}{3 + \sqrt[3]{3} + \sqrt[3]{9}} = 3 - \sqrt[3]{9}