Question

RACIONALIZAÇÂO


(raiz de 5-2) sobre (raiz de 5+2)

Answer 1

$\dfrac{\sqrt{5}-2}{\sqrt{5}+2}\\ \\ =\dfrac{\left(\sqrt{5}-2 \right )\cdot \left(\sqrt{5}-2 \right )}{\left(\sqrt{5}+2 \right )\cdot \left(\sqrt{5}-2 \right )}\\ \\ =\dfrac{\left(\sqrt{5}-2 \right )^{2}}{\left(\sqrt{5} \right )^{2}-\left(2 \right )^{2}}\\ \\ =\dfrac{\left(\sqrt{5} \right )^{2}-2\cdot \left(\sqrt{5} \right )\cdot \left(2 \right )+\left(2 \right )^{2}}{\left(\sqrt{5} \right )^{2}-\left(2 \right )^{2}}\\ \\ =\dfrac{5-4\sqrt{5}+4}{5-4}\\ \\ =\dfrac{9-4\sqrt{5}}{1}\\ \\ =9-4\sqrt{5}$