803 Вправа 803Алгебра 8 клас Бевз 2025 · § 16 · стор. 153

803. Виконай дії.

Формули: ${\displaystyle {(a\pm b)}^2=}$${\displaystyle a^2\pm 2ab+b^2}$.

а) ${\displaystyle {(1+\sqrt{3})}^2=}$${\displaystyle 1+2\sqrt{3}+3=}$${\displaystyle 4+2\sqrt{3}}$;

б) ${\displaystyle {(3\sqrt{2}+5\sqrt{3})}^2}$=

=${\displaystyle 18+2\cdot 3\sqrt{2}\cdot 5\sqrt{3}+75=}$${\displaystyle 93+30\sqrt{6}}$;

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

=${\displaystyle 5-2\sqrt{10}+2+2\sqrt{10}=}$${\displaystyle 7}$;

г) ${\displaystyle {(\sqrt{5}+1)}^2-\sqrt{20}=}$${\displaystyle 5+2\sqrt{5}+1-2\sqrt{5}=}$${\displaystyle 6}$.