Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 64

\[\boxed{\mathbf{64}\mathbf{.}}\]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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