Вычислить:[latex] \sqrt{2,1*1,9} ( \sqrt{ \frac{19}{21} }- \sqrt{ \frac{21}{19} } ) [/latex]

[latex] \sqrt{2.1*1.9} ( \sqrt{ \frac{19}{21} } - \sqrt{ \frac{21}{19} } )= \\ \\ = \sqrt{ \frac{21*19}{10^2} } (\sqrt{ \frac{19}{21} } - \sqrt{ \frac{21}{19} })= \frac{ \sqrt{21*19} }{10} ( \frac{ \sqrt{399} }{21} - \frac{ \sqrt{399} }{19} )= \\ \\ = \frac{ \sqrt{399} }{10} * \frac{(19 \sqrt{399}-21 \sqrt{399}) }{21*19} = \frac{-2*399}{10*21*19} =-0.2[/latex] Ответ: [latex]-0.2[/latex]

[latex] \sqrt{2.1*1.9} *( \sqrt{ \frac{19}{21} } - \sqrt{ \frac{21}{19} } )=-00.2 \\ \\ 1) \sqrt{ \frac{19}{21} } - \sqrt{ \frac{21}{19} }= \frac{ \sqrt{19} }{ \sqrt{21} } - \frac{ \sqrt{21} }{ \sqrt{19} } = \frac{ \sqrt{19} * \sqrt{19} - \sqrt{21} * \sqrt{21} }{ \sqrt{19} * \sqrt{21} } = \frac{19-21}{ \sqrt{399} } =- \frac{2}{ \sqrt{399} } \\ \\ 2) \sqrt{2.1*1.9} = \sqrt{3.99} \\ \\ 3) \sqrt{3.99} *(-\frac{2}{ \sqrt{399} })=- \frac{2* \sqrt{3.99} }{ \sqrt{399} } =-2*0.01=-0.02[/latex]