Упр.37.28 ГДЗ Мордкович 10-11 класс (Алгебра)

а) (4 * 3^1/2) / (3^1/2 — 3);
б) (a^1/2 — b^1/2) / (a — b);
в) (x + x^1/2) / 2x;
г) (p^1/2 — 5) / (p — 25).

1. а)

   $$\frac{4\cdot 3^{1/2}}{3^{1/2}-3}=\frac{4\cdot 3^{1/2}}{3^{1/2}(1-3^{1/2})}=\frac{4}{1-\sqrt{3}}.$$

2. б)

   $$\frac{a^{1/2}-b^{1/2}}{a-b}=\frac{a^{1/2}-b^{1/2}}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}=\frac{1}{a^{1/2}+b^{1/2}}=\frac{1}{\sqrt{a}+\sqrt{b}}.$$

3. в)

   $$\frac{x+x^{1/2}}{2x}=\frac{x^{1/2}(x^{1/2}+1)}{2(x^{1/2})^2}=\frac{x^{1/2}+1}{2x^{1/2}}=\frac{\sqrt{x}+1}{2\sqrt{x}}.$$

4. г)

   $$\frac{p^{1/2}-5}{p-25}=\frac{p^{1/2}-5}{(p^{1/2}-5)(p^{1/2}+5)}=\frac{1}{p^{1/2}+5}=\frac{1}{\sqrt{p}+5}.$$

Ответ

а) $$\frac{4}{1-\sqrt{3}}$$; б) $$\frac{1}{\sqrt{a}+\sqrt{b}}$$; в) $$\frac{\sqrt{x}+1}{2\sqrt{x}}$$; г) $$\frac{1}{\sqrt{p}+5}$$.