Упр.102 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (3v6+5v8-4v32)•v2-v108;
2) (v5+7v2)(7v2-v5)-(v10-2v5)^2;
3) (7-v3)^2+(4+v3)^2;
4) (v(7-4v3) +v(7+4v3) )^2.

1. $$\left(3\sqrt6+5\sqrt8-4\sqrt{32}\right)\cdot\sqrt2-\sqrt{108}$$
   $$=\left(3\sqrt6+5\cdot2\sqrt2-4\cdot4\sqrt2\right)\cdot\sqrt2-6\sqrt3$$
   $$=\left(3\sqrt6+10\sqrt2-16\sqrt2\right)\cdot\sqrt2-6\sqrt3$$
   $$=\left(3\sqrt6-6\sqrt2\right)\cdot\sqrt2-6\sqrt3$$
   $$=3\sqrt{12}-12-6\sqrt3=3\cdot2\sqrt3-12-6\sqrt3=-12.$$

2. $$\left(\sqrt5+7\sqrt2\right)\left(7\sqrt2-\sqrt5\right)-\left(\sqrt{10}-2\sqrt5\right)^2$$
   $$=7\sqrt{10}-5+98-7\sqrt{10}-\left(10-4\sqrt{50}+20\right)$$
   $$=93-\left(30-4\sqrt{50}\right)=93-30+4\sqrt{50}$$
   $$=63+4\cdot5\sqrt2=63+20\sqrt2.$$

3. $$\left(7-\sqrt3\right)^2+\left(4+\sqrt3\right)^2$$
   $$=\left(49-14\sqrt3+3\right)+\left(16+8\sqrt3+3\right)$$
   $$=52-14\sqrt3+19+8\sqrt3=71-6\sqrt3.$$

4. $$\left(\sqrt{7-4\sqrt3}+\sqrt{7+4\sqrt3}\right)^2$$
   $$=\left(7-4\sqrt3\right)+2\sqrt{\left(7-4\sqrt3\right)\left(7+4\sqrt3\right)}+\left(7+4\sqrt3\right)$$
   $$=14+2\sqrt{49-48}=14+2=16.$$

Ответ

1) $$-12$$; 2) $$63+20\sqrt2$$; 3) $$71-6\sqrt3$$; 4) $$16$$.