№ 17 ЗПС Алгебра = № 17 ЗПС Математика
Обчисліть:
1. $\frac{\frac{\sqrt5+\sqrt3}{\sqrt3}-\frac{\sqrt5+\sqrt3}{\sqrt5}}{\frac{\sqrt5-\sqrt3}{\sqrt3}+\frac{\sqrt5-\sqrt3}{\sqrt5}};$
2. $(\sqrt3+\sqrt2+1)\cdot$
$\cdot(\sqrt3+\sqrt2-1)\cdot$
$\cdot(\sqrt3+1-\sqrt2)\cdot$
$\cdot(1+\sqrt2-\sqrt3).$
Розв'язок:
1. $\frac{\frac{\sqrt5+\sqrt3}{\sqrt3}-\frac{\sqrt5+\sqrt3}{\sqrt5}}{\frac{\sqrt5-\sqrt3}{\sqrt3}+\frac{\sqrt5-\sqrt3}{\sqrt5}}=$
$= \frac{\sqrt5(\sqrt5+\sqrt3)-\sqrt3(\sqrt5+\sqrt3)}{\sqrt{15}}·$
$· \frac{\sqrt{15}}{\sqrt5(\sqrt5-\sqrt3)+\sqrt3(\sqrt5-\sqrt3)}=$
$= \frac{5+\sqrt{15}-\sqrt{15}-3}{5-\sqrt{15}+\sqrt{15}-3}=1;$
