№ 3.32 Алгебра = № 8.32 Математика
Обчисліть: $\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}+\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}$
Розв’язок:
$\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}+\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}=$
$=\frac{(\sqrt{5}-\sqrt{2})^{2}+(\sqrt{5}+\sqrt{2})^{2}}{5-2}=$
$=\frac{5-2\sqrt{10}+2+5+2\sqrt{10}+2}{3}=$
$=\frac{14}{3}=4\frac{2}{3}$