Упр.102 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (2v3+6v20-7v45)•v5-v60;
2) (v7-2v3)(2v3+v7)-(v6-3v2)^2;
3) (5-v2)^2+(3+v2)^2;
4) (v(9-4v5) -v(9+4v5) )^2.

1. $$\left(2\sqrt{3}+6\sqrt{20}-7\sqrt{45}\right)\cdot \sqrt{5}-\sqrt{60}$$
   $$=\left(2\sqrt{3}+6\cdot 2\sqrt{5}-7\cdot 3\sqrt{5}\right)\cdot \sqrt{5}-2\sqrt{15}$$
   $$=\left(2\sqrt{3}+12\sqrt{5}-21\sqrt{5}\right)\cdot \sqrt{5}-2\sqrt{15}$$
   $$=\left(2\sqrt{3}-9\sqrt{5}\right)\cdot \sqrt{5}-2\sqrt{15}$$
   $$=2\sqrt{15}-45-2\sqrt{15}=-45.$$

2. $$\left(\sqrt{7}-2\sqrt{3}\right)\left(2\sqrt{3}+\sqrt{7}\right)-\left(\sqrt{6}-3\sqrt{2}\right)^2$$
   $$=2\sqrt{21}+7-12- \left(6-6\sqrt{12}+18\right)$$
   $$=2\sqrt{21}-5-24+6\sqrt{12}$$
   $$=2\sqrt{21}-29+6\cdot 2\sqrt{3}$$
   $$=2\sqrt{21}-29+12\sqrt{3}.$$

3. $$\left(5-\sqrt{2}\right)^2+\left(3+\sqrt{2}\right)^2$$
   $$=25-10\sqrt{2}+2+9+6\sqrt{2}+2$$
   $$=38-4\sqrt{2}.$$

4. $$\left(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\right)^2$$
   $$=\left(\sqrt{9-4\sqrt{5}}\right)^2-2\sqrt{(9-4\sqrt{5})(9+4\sqrt{5})}+\left(\sqrt{9+4\sqrt{5}}\right)^2$$
   $$=9-4\sqrt{5}-2\sqrt{81-80}+9+4\sqrt{5}$$
   $$=18-2\sqrt{1}=18-2=16.$$

Ответ

1) $$-45$$; 2) $$2\sqrt{21}+12\sqrt{3}-29$$; 3) $$38-4\sqrt{2}$$; 4) $$16$$.