Question

Al racionalizar la expresión M se obtiene:
M=10/(2-∛12+∛18)

Answer 1

$Analizamos$

$M=\dfrac{10}{2-\sqrt[3]{12}+\sqrt[3]{18}};M=\dfrac{10}{\sqrt[3]{2^{3}} -\sqrt[3]{12}+\sqrt[3]{18}}$

$M=\dfrac{10}{\sqrt[3]{2^{3}} -\sqrt[3]{12}+\sqrt[3]{18}};M=\dfrac{10}{\sqrt[3]{2}[\sqrt[3]{2^{2}}-\sqrt[3]{6}+\sqrt[3]{9}]}$

$M=\dfrac{10}{\sqrt[3]{2}[\sqrt[3]{2^{2}}-\sqrt[3]{6}+\sqrt[3]{9}]};M=\dfrac{10}{\sqrt[3]{2}[\sqrt[3]{2^{2}}-\sqrt[3]{6}+\sqrt[3]{3^{2}}]}$

$M=\dfrac{10}{\sqrt[3]{2}[\sqrt[3]{2}^{2}-\sqrt[3]{2.3}+\sqrt[3]{3}^{2}]}.\dfrac{[\sqrt[3]{2}+\sqrt[3]{3}]}{[\sqrt[3]{2}+\sqrt[3]{3}]}$

$M=\dfrac{10[\sqrt[3]{2}+\sqrt[3]{3}]}{\sqrt[3]{2}[2+3]};M=\dfrac{2[\sqrt[3]{2}+\sqrt[3]{3}]}{\sqrt[3]{2}}$

$M=\dfrac{2[\sqrt[3]{2}+\sqrt[3]{3}]}{\sqrt[3]{2}}.\dfrac{[\sqrt[3]{2}^{2}]}{[\sqrt[3]{2}^{2}]}$

$M=[\sqrt[3]{2}+\sqrt[3]{3}][\sqrt[3]{2}^{2}]:M=2+\sqrt[3]{12}$

$\mathbb{AUTOR}: \mathrm{SMITH \ VALDEZ}$