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

1. а) $$\frac{4\cdot 3^{1/2}}{3^{1/2}-3}$$
2. б) $$\frac{a^{1/2}-b^{1/2}}{a-b}$$
3. в) $$\frac{x+x^{1/2}}{2x}$$
4. г) $$\frac{p^{1/2}-5}{p-25}$$

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

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

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

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) $$\frac{1}{\sqrt{p}+5}$$.