Question

(√¯6+√¯3)²/3 tenho a resposta,mas nao sei a resolução

resposta= 3+2√¯2

Answer 1

$\mathtt{\dfrac{(\sqrt{6}+\sqrt{3})^2}{3}}\\\\\\ =\mathtt{\dfrac{(\sqrt{6}+\sqrt{3})\cdot (\sqrt{6}+\sqrt{3})}{3}}\\\\\\ =\mathtt{\dfrac{(\sqrt{6}+\sqrt{3})\cdot \sqrt{6}+(\sqrt{6}+\sqrt{3})\cdot \sqrt{3}}{3}}\\\\\\ =\mathtt{\dfrac{\sqrt{6}\cdot \sqrt{6}+\sqrt{3}\cdot \sqrt{6}+\sqrt{6}\cdot \sqrt{3}+\sqrt{3}\cdot \sqrt{3}}{3}}\\\\\\ =\mathtt{\dfrac{(\sqrt{6})^2+2\cdot \sqrt{6}\cdot \sqrt{3}+(\sqrt{3})^2}{3}}$

$=\mathtt{\dfrac{6+2\sqrt{6\cdot 3}+3}{3}}\\\\\\ =\mathtt{\dfrac{9+2\sqrt{18}}{3}}\\\\\\ =\mathtt{\dfrac{9+2\sqrt{2\cdot 9}}{3}}\\\\\\ =\mathtt{\dfrac{9+2\sqrt{2\cdot 3^2}}{3}}\\\\\\ =\mathtt{\dfrac{9+2\sqrt{2}\cdot\sqrt{3^2}}{3}}\\\\\\ =\mathtt{\dfrac{9+2\sqrt{2}\cdot 3}{3}}$

$=\mathtt{\dfrac{3\cdot 3+2\sqrt{2}\cdot 3}{3}}\\\\\\ =\mathtt{\dfrac{\diagup\!\!\!\! 3\cdot (3+2\sqrt{2})}{\diagup\!\!\!\! 3}}$

$=\boxed{\begin{array}{c}\mathtt{3+2\sqrt{2}}\end{array}}$   <———    esta é a resposta.


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Bons estudos! :-)