Упр.17.24 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1) v2/(v2+1); 2) 19/(2v5-1); 3) 1/(va-vb); 4) (v3+1)/(v3-1).

1. $$\frac{\sqrt{2}}{\sqrt{2}+1}=\frac{\sqrt{2}(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{2-\sqrt{2}}{2-1}=2-\sqrt{2}.$$

2. $$\frac{19}{2\sqrt{5}-1}=\frac{19(2\sqrt{5}+1)}{(2\sqrt{5}-1)(2\sqrt{5}+1)}=\frac{19(2\sqrt{5}+1)}{4\cdot 5-1}=\frac{19(2\sqrt{5}+1)}{19}=2\sqrt{5}+1.$$

3. $$\frac{1}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt{a}+\sqrt{b}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}=\frac{\sqrt{a}+\sqrt{b}}{a-b}.$$

4. $$\frac{\sqrt{3}+1}{\sqrt{3}-1}=\frac{(\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}=\frac{3+2\sqrt{3}+1}{3-1}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3}.$$

Ответ

1) $$2-\sqrt{2}$$; 2) $$2\sqrt{5}+1$$; 3) $$\frac{\sqrt{a}+\sqrt{b}}{a-b}$$; 4) $$2+\sqrt{3}$$.