Question

Решите.....................................

Answer 1

$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}} + \frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}} =\frac{(\sqrt{7}-\sqrt{5})(\sqrt{7}-\sqrt{5})}{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})}+\frac{(\sqrt{7}+\sqrt{5})(\sqrt{7}+\sqrt{5})}{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5})}=\frac{(\sqrt{7}-\sqrt{5})^{2}}{(\sqrt{7})^{2}-(\sqrt{5})^{2}}+\frac{(\sqrt{7}+\sqrt{5})^{2}}{(\sqrt{7})^{2}-(\sqrt{5})^{2}}=\frac{(\sqrt{7}-\sqrt{5})^{2}+(\sqrt{7}+\sqrt{5})^{2}}{(\sqrt{7})^{2}-(\sqrt{5})^{2})}=\frac{(\sqrt{7})^{2}-2\sqrt{7}\sqrt{5}+(\sqrt{5})^{2}+(\sqrt{7})^{2}+2\sqrt{7}\sqrt{5}+(\sqrt{5})^{2}}{(\sqrt{7})^{2}-(\sqrt{5})^{2}}=\\=\frac{7-2\sqrt{35}+5+7+2\sqrt{35}+5}{7-5}=\frac{24}{2}=12$