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]