ГДЗ по алгебре и начала математического анализа 10 класс Алимов Задание 1282

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\[1)\ 6n \bullet \sqrt{\frac{m}{2n}} \bullet \sqrt{18mn} =\]

\[= \sqrt{36n^{2} \bullet \frac{m}{2n} \bullet 18mn} =\]

\[= \sqrt{18n^{2} \bullet m^{2} \bullet 18} = 18mn;\]

\[2)\ \frac{a - 1}{a^{\frac{3}{4}} + a^{\frac{1}{2}}} \bullet \frac{a^{\frac{1}{2}} + a^{\frac{1}{4}}}{a^{\frac{1}{2}} + 1} \bullet a^{\frac{1}{4}} =\]

\[= \frac{\left( \sqrt{a} - 1 \right)\left( \sqrt{a} + 1 \right)}{a^{\frac{1}{2}} \bullet \left( a^{\frac{1}{4}} + 1 \right)} \bullet \frac{a^{\frac{1}{4}} \bullet \left( a^{\frac{1}{4}} + 1 \right)}{\sqrt{a} + 1} \bullet a^{\frac{1}{4}} =\]

\[= \frac{\sqrt{a} - 1}{a^{\frac{1}{2}}} \bullet a^{\frac{1}{4}} \bullet a^{\frac{1}{4}} =\]

\[= \frac{\sqrt{a} - 1}{a^{\frac{1}{2}}} \bullet a^{\frac{1}{2}} = \sqrt{a} - 1.\]