Question

raiz de 3 mais 1
dividido por raiz de 3 menos 1

Answer 1

Usando o fato de que
$a^b\cdot \:a^c=a^{b+c}\\\\ (a+b)^2=a^2+2ab+b^2\\\\ \left(a-b\right)\left(a+b\right)=a^2-b^2$


Conseguimos calcular

$\dfrac{\sqrt{3}+1}{\sqrt{3}-1} = \dfrac{(\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)} = \\\\\\ = \dfrac{(\sqrt{3})^2+2\sqrt{3}\cdot \:1+1^2}{(\sqrt{3})^2-1^2} \\\\\\ = \dfrac{2\sqrt{3}+4}{2}\\\\\\ = \dfrac{\not{2}(2+\sqrt{3})}{\not{2}}\\\\\\ = \framebox{ 2+\sqrt{3} }$