Задача 60665 Надо...

61378e12bdb7e738ec3811b0

07.09.2021 19:08:15

Надо упростить
[m]\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}+\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}[/m]

5f3ea7e3faf909182968ddd9

07.09.2021 19:58:17

★

[m]\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}+\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}=\frac{(\sqrt{7}+\sqrt{3})^2}{(\sqrt{7}-\sqrt{3})\cdot (\sqrt{7}+\sqrt{3})}+\frac{(\sqrt{7}-\sqrt{3})^2}{(\sqrt{7}+\sqrt{3})\cdot(\sqrt{7}-\sqrt{3}) }=\frac{(\sqrt{7}+\sqrt{3})^2+(\sqrt{7}-\sqrt{3})^2}{(\sqrt{7}+\sqrt{3})\cdot(\sqrt{7}-\sqrt{3}) }=[/m]

[m]=\frac{7+2\sqrt{7}\cdot \sqrt{3}+3+7-2\sqrt{7}\cdot \sqrt{3}+3}{(\sqrt{7})^2-(\sqrt{3})^2 }=\frac{20}{4}=5[/m]