Упр.546 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

Вычислить:

1. $$\left(6-3\sqrt{5}\right)\left(6+3\sqrt{5}\right)$$;
2. $$\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)$$;
3. $$\left(3\sqrt{5}-2\sqrt{20}\right)\sqrt{5}$$;
4. $$\left(1-\sqrt{3}\right)^2+\left(1+\sqrt{3}\right)^2$$.

1. $$\begin{aligned} (6-3\sqrt{5})(6+3\sqrt{5})&=6^2-(3\sqrt{5})^2\\ &=36-9\cdot 5\\ &=36-45\\ &=-9 \end{aligned}$$
2. $$\begin{aligned} (\sqrt{5}-1)(\sqrt{5}+1)&=(\sqrt{5})^2-1^2\\ &=5-1\\ &=4 \end{aligned}$$
3. $$\begin{aligned} (3\sqrt{5}-2\sqrt{20})\sqrt{5}&=3\sqrt{25}-2\sqrt{100}\\ &=3\cdot 5-2\cdot 10\\ &=15-20\\ &=-5 \end{aligned}$$
4. $$\begin{aligned} (1-\sqrt{3})^2+(1+\sqrt{3})^2&=(1-2\sqrt{3}+3)+(1+2\sqrt{3}+3)\\ &=4-2\sqrt{3}+4+2\sqrt{3}\\ &=8 \end{aligned}$$

Ответ

1) $$-9$$; 2) $$4$$; 3) $$-5$$; 4) $$8$$.