Question

Calcule racionalizando

Answer 1

Resposta:

a) $\frac{8\sqrt{7}}{7}$

b) $2$

Explicação passo-a-passo:

a) $\sqrt{7}+\frac{1}{\sqrt{7}} = \sqrt{7}\times \frac{\sqrt{7}}{\sqrt{7}}+\frac{1}{\sqrt{7}} = \frac{(\sqrt{7})^2}{\sqrt{7}}+\frac{1}{\sqrt{7}}=\frac{(\sqrt{7})^2+1}{\sqrt{7}}=\frac{7+1}{\sqrt{7}}=\frac{8}{\sqrt{7}}= \frac{8}{\sqrt{7}}\times \frac{\sqrt{7}}{\sqrt{7}}=\frac{8\sqrt{7}}{7}$

b) $\frac{1}{2+\sqrt{2}}+\frac{1}{2-\sqrt{2}} = \frac{1}{2+\sqrt{2}}\times \frac{2-\sqrt{2}}{2-\sqrt{2}} + \frac{1}{2-\sqrt{2}} \times \frac{2+\sqrt{2}}{2+\sqrt{2}} = \frac{(2-\sqrt{2})+(2+\sqrt{2})}{(2+\sqrt{2})(2-\sqrt{2})} = \frac{4}{4-(\sqrt{2})^2} =\frac{4}{4-2}=\frac{4}{2}=2$