Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 63

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\[1)\ x^{\frac{1}{2}} + x = x^{\frac{1}{2}} + x^{1} =\]

\[= x^{\frac{1}{2}} + x^{\frac{1}{2} + \frac{1}{2}} = x^{\frac{1}{2}} + x^{\frac{1}{2}} \bullet x^{\frac{1}{2}} =\]

\[= x^{\frac{1}{2}} \bullet \left( 1 + x^{\frac{1}{2}} \right)\]

\[2)\ \left( \text{ab} \right)^{\frac{1}{3}} + \left( \text{ac} \right)^{\frac{1}{3}} =\]

\[= a^{\frac{1}{3}} \bullet b^{\frac{1}{3}} + a^{\frac{1}{3}} \bullet c^{\frac{1}{3}} =\]

\[= a^{\frac{1}{3}} \bullet \left( b^{\frac{1}{3}} + c^{\frac{1}{3}} \right)\]

\[3)\ y^{\frac{3}{4}} - y^{\frac{1}{3}} = y^{\frac{9}{12}} - y^{\frac{4}{12}} =\]

\[= y^{\frac{4}{12} + \frac{5}{12}} - y^{\frac{4}{12}} =\]

\[= y^{\frac{4}{12}} \bullet y^{\frac{5}{12}} - y^{\frac{4}{12}} =\]

\[= y^{\frac{4}{12}} \bullet \left( y^{\frac{5}{12}} - 1 \right) =\]

\[= y^{\frac{1}{3}} \bullet \left( y^{\frac{5}{12}} - 1 \right)\]

\[4)\ 12xy^{\frac{1}{2}} - 3x^{\frac{1}{2}}y =\]

\[= 12x^{\frac{1}{2} + \frac{1}{2}}y^{\frac{1}{2}} - 3x^{\frac{1}{2}}y^{\frac{1}{2} + \frac{1}{2}} =\]

\[= 4x^{\frac{1}{2}} \bullet 3x^{\frac{1}{2}}y^{\frac{1}{2}} - 3x^{\frac{1}{2}}y^{\frac{1}{2}} \bullet y^{\frac{1}{2}} =\]

\[= 3x^{\frac{1}{2}}y^{\frac{1}{2}} \bullet \left( 4x^{\frac{1}{2}} - y^{\frac{1}{2}} \right)\]