Question

Si : a - b = b - c = $\sqrt[3]{3}$
Calcular:
S=$\frac{ (a-b)^{3} +(b-c)^{3} +(a-c)^{3}}{10}$

Answer 1

EL único valor que nos falta es a - c, esto lo hallaremos de la siguiente manera

                                         $\begin{array}{ccc}\\\boldsymbol{\sf{a-b=\sqrt[3]{3}}}&(+)&\\\\\boldsymbol{\sf{b-c=\sqrt[3]{3}}}&&\\\rule{140pt}{0.2ex}\\\sf{(a-\not b)+(\not b-c)=\sqrt[3]{3}+\sqrt[3]{3}}&&\\\\\boxed{\sf{a-c=2\sqrt[3]{3}}}&&\end{array}$

Entonces reemplazamos en lo que nos piden

                                      $\begin{array}{c}\\\sf{S=\dfrac{(a-b)^3+(b-c)^2+(a-c)^2}{10}}\\\\\sf{S=\dfrac{(\sqrt[3]{3})^3+(\sqrt[3]{3})^3+(2\sqrt[3]{3})^3}{10}}\\\\\sf{S=\dfrac{(\sqrt[\not 3]{3})^{\not 3}+(\sqrt[\not 3]{3})^{\not 3}+(2^3)(\sqrt[\not 3]{3})^{\not 3}}{10}}\\\\\sf{S=\dfrac{3+3+8(3)}{10}}\\\\\sf{S=\dfrac{30}{10}}\\\\\boxed{\boxed{\boldsymbol{\red{\sf{S=3}}}}}\end{array}$

Rpta. El valor de S es 3.

                                               $\boxed{\sf{{R}}\quad\raisebox{10pt}{ \sf{\red{O}} }\!\!\!\!\raisebox{-10pt}{ \sf{\red{O}} }\quad\raisebox{15pt}{ \sf{{G}} }\!\!\!\!\raisebox{-15pt}{ \sf{{G}} }\quad\raisebox{15pt}{ \sf{\red{H}} }\!\!\!\!\raisebox{-15pt}{ \sf{\red{H}} }\quad\raisebox{10pt}{ \sf{{E}} }\!\!\!\!\raisebox{-10pt}{ \sf{{E}} }\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}$