Упр.102 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (4v7+7v12-2v192)•v3-v84;
2) (2v5-v15)(v15+2v5)-(v10-5v2)^2;
3) (8-v6)^2+(5+v6)^2;
4) (v(8+2v7) +v(8-2v7) )^2.

1. $$\left(4\sqrt7+7\sqrt{12}-2\sqrt{192}\right)\cdot\sqrt3-\sqrt{84}$$

   $$= \left(4\sqrt7+7\cdot 2\sqrt3-2\cdot 8\sqrt3\right)\cdot\sqrt3-2\sqrt{21}$$

   $$= \left(4\sqrt7+14\sqrt3-16\sqrt3\right)\cdot\sqrt3-2\sqrt{21}$$

   $$= \left(4\sqrt7-2\sqrt3\right)\cdot\sqrt3-2\sqrt{21}$$

   $$=4\sqrt{21}-2\cdot 3-2\sqrt{21}=2\sqrt{21}-6$$

2. $$\left(2\sqrt5-\sqrt{15}\right)\left(\sqrt{15}+2\sqrt5\right)-\left(\sqrt{10}-5\sqrt2\right)^2$$

   $$=(2\sqrt5)^2-(\sqrt{15})^2-\left(10-10\sqrt{20}+25\cdot 2\right)$$

   $$=4\cdot 5-15-\left(10-10\sqrt{20}+50\right)$$

   $$=20-15-(60-10\sqrt{20})=5-60+10\sqrt{20}$$

   $$=10\sqrt{4\cdot 5}-55=10\cdot 2\sqrt5-55=20\sqrt5-55$$

3. $$\left(8-\sqrt6\right)^2+\left(5+\sqrt6\right)^2$$

   $$=64-16\sqrt6+6+25+10\sqrt6+6$$

   $$=101-6\sqrt6$$

4. $$\left(\sqrt{8+2\sqrt7}+\sqrt{8-2\sqrt7}\right)^2$$

   $$=\left(\sqrt{8+2\sqrt7}\right)^2+2\sqrt{(8+2\sqrt7)(8-2\sqrt7)}+\left(\sqrt{8-2\sqrt7}\right)^2$$

   $$=8+2\sqrt7+2\sqrt{64-28}+8-2\sqrt7$$

   $$=16+2\sqrt{36}=16+12=28$$

Ответ

$$1)\ 2\sqrt{21}-6;\quad 2)\ 20\sqrt5-55;\quad 3)\ 101-6\sqrt6;\quad 4)\ 28.$$