Задание 5 Параграф 17 ГДЗ Рабочая тетрадь 2 Мерзляк Полонский 8 класс (Алгебра)

1) (3-v5)(v5+4);
2) (6v2+v11)(2v11-v2);
3) (3v7-2v6)(3v7+2v6);
4) (v31-4)(v31+4);
5) (9va+2v5b)(9va-2v5b);
6) (7v2+2v13)^2;
7) (v5-2)^2;
8) (2v7+3)^2.

1. $$\begin{aligned} (3-\sqrt{5})(\sqrt{5}+4) &= 3\sqrt{5}+12-(\sqrt{5})^2-4\sqrt{5} \\ &= 3\sqrt{5}-4\sqrt{5}+12-5 \\ &= 7-\sqrt{5}. \end{aligned}$$
2. $$\begin{aligned} (6\sqrt{2}+\sqrt{11})(2\sqrt{11}-\sqrt{2}) &= 6\sqrt{2}\cdot 2\sqrt{11}-6\sqrt{2}\cdot \sqrt{2}+\sqrt{11}\cdot 2\sqrt{11}-\sqrt{11}\cdot \sqrt{2} \\ &= 12\sqrt{22}-12+22-\sqrt{22} \\ &= 11\sqrt{22}+10. \end{aligned}$$
3. $$\begin{aligned} (3\sqrt{7}-2\sqrt{6})(3\sqrt{7}+2\sqrt{6}) &= (3\sqrt{7})^2-(2\sqrt{6})^2 \\ &= 9\cdot 7-4\cdot 6 \\ &= 63-24=39. \end{aligned}$$
4. $$\begin{aligned} (\sqrt{31}-4)(\sqrt{31}+4) &= (\sqrt{31})^2-4^2 \\ &= 31-16=15. \end{aligned}$$
5. $$\begin{aligned} (9\sqrt{a}+2\sqrt{5b})(9\sqrt{a}-2\sqrt{5b}) &= (9\sqrt{a})^2-(2\sqrt{5b})^2 \\ &= 81a-4\cdot 5b \\ &= 81a-20b. \end{aligned}$$
6. $$\begin{aligned} (7\sqrt{2}+2\sqrt{13})^2 &= (7\sqrt{2})^2+2\cdot 7\sqrt{2}\cdot 2\sqrt{13}+(2\sqrt{13})^2 \\ &= 49\cdot 2+28\sqrt{26}+4\cdot 13 \\ &= 98+28\sqrt{26}+52 \\ &= 150+28\sqrt{26}. \end{aligned}$$
7. $$\begin{aligned} (\sqrt{5}-2)^2 &= (\sqrt{5})^2-2\cdot \sqrt{5}\cdot 2+2^2 \\ &= 5-4\sqrt{5}+4 \\ &= 9-4\sqrt{5}. \end{aligned}$$
8. $$\begin{aligned} (2\sqrt{7}+3)^2 &= (2\sqrt{7})^2+2\cdot 2\sqrt{7}\cdot 3+3^2 \\ &= 4\cdot 7+12\sqrt{7}+9 \\ &= 37+12\sqrt{7}. \end{aligned}$$

Ответ

1) $$7-\sqrt{5}$$; 2) $$11\sqrt{22}+10$$; 3) $$39$$; 4) $$15$$; 5) $$81a-20b$$; 6) $$150+28\sqrt{26}$$; 7) $$9-4\sqrt{5}$$; 8) $$37+12\sqrt{7}$$.