Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 476

\[\boxed{\mathbf{476}.}\]

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

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

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

\[= \left( y^{\frac{1}{3}} + 1 \right)\left( y^{\frac{1}{3}} - 1 \right);\]

\[3)\ a^{\frac{1}{3}} - b^{\frac{1}{3}} = a^{\frac{2}{6}} - b^{\frac{2}{6}} = \left( a^{\frac{1}{6}} \right)^{2} -\]

\[- \left( b^{\frac{1}{6}} \right)^{2} = \left( a^{\frac{1}{6}} + b^{\frac{1}{6}} \right)\left( a^{\frac{1}{6}} - b^{\frac{1}{6}} \right);\]

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

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

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

\[5)\ 4a^{\frac{1}{2}} - b^{\frac{1}{2}} = 2^{2}a^{\frac{2}{4}} - b^{\frac{2}{4}} =\]

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

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

\[6)\ 0,01m^{\frac{1}{6}} - n^{\frac{1}{6}} = (0,1)^{2}m^{\frac{2}{12}} -\]

\[- n^{\frac{2}{12}} = \left( 0,1m^{\frac{1}{12}} \right)^{2} - \left( n^{\frac{1}{12}} \right)^{2} =\]

\[= \left( 0,1m^{\frac{1}{12}} + n^{\frac{1}{12}} \right)\]

\[\left( 0,1m^{\frac{1}{12}} - n^{\frac{1}{12}} \right);\]