830 Вправа 830Алгебра 8 клас Бевз 2025 · § 16 · стор. 156

830. Спрости вираз.

а) ${\displaystyle {(2-\sqrt{3})}^2+{(2+\sqrt{3})}^2}$=

=${\displaystyle 4-4\sqrt{3}+3+4+4\sqrt{3}+3=}$${\displaystyle 14}$;

б) ${\displaystyle (7-2\sqrt{10}){(\sqrt{2}+\sqrt{5})}^2}$=

=${\displaystyle (7-2\sqrt{10})(7+2\sqrt{10})=}$${\displaystyle 49-40=}$${\displaystyle 9}$;

в) ${\displaystyle \sqrt{9-4\sqrt{2}}\cdot \sqrt{9+4\sqrt{2}}}$=

=${\displaystyle \sqrt{(9-4\sqrt{2})(9+4\sqrt{2})}=}$${\displaystyle \sqrt{81-32}=}$${\displaystyle \sqrt{49}=}$${\displaystyle 7}$;

г) ${\displaystyle {(\sqrt{5+\sqrt{24}}+\sqrt{5-\sqrt{24}})}^2}$=

=${\displaystyle 5+\sqrt{24}+2\sqrt{(5+\sqrt{24})(5-\sqrt{24})}+5-\sqrt{24}}$=

=${\displaystyle 10+2\sqrt{25-24}=}$${\displaystyle 12}$.