Ответы
Ответ дал:
0
6)
![( frac{a^{-1}-b^{-1}}{a^{-3}+b^{-3}}: frac{a^2b^2}{(a+b)^2-3ab}+1 )^{-1}-0.5= \ \
=( frac{ frac{1}{a}- frac{1}{b}}{ frac{1}{a^3}+ frac{1}{b^3} }* frac{a^2+2ab+b^2-3ab}{a^2b^2}+1 )^{-1}-0.5= \ \
=( frac{ frac{b-a}{ab} }{ frac{b^3+a^3}{a^3b^3} }* frac{a^2-ab+b^2}{a^2b^2} +1 )^{-1}-0.5= \ \
=( frac{(b-a)a^3b^3}{ab(a^3+b^3)}* frac{a^2-ab+b^2}{a^2b^2}+1 )^{-1}-0.5= \ \
=( frac{(b-a)}{(a+b)(a^2-ab+b^2)}* frac{a^2-ab+b^2}{1} +1 )^{-1}-0.5= \ \
( frac{a^{-1}-b^{-1}}{a^{-3}+b^{-3}}: frac{a^2b^2}{(a+b)^2-3ab}+1 )^{-1}-0.5= \ \
=( frac{ frac{1}{a}- frac{1}{b}}{ frac{1}{a^3}+ frac{1}{b^3} }* frac{a^2+2ab+b^2-3ab}{a^2b^2}+1 )^{-1}-0.5= \ \
=( frac{ frac{b-a}{ab} }{ frac{b^3+a^3}{a^3b^3} }* frac{a^2-ab+b^2}{a^2b^2} +1 )^{-1}-0.5= \ \
=( frac{(b-a)a^3b^3}{ab(a^3+b^3)}* frac{a^2-ab+b^2}{a^2b^2}+1 )^{-1}-0.5= \ \
=( frac{(b-a)}{(a+b)(a^2-ab+b^2)}* frac{a^2-ab+b^2}{1} +1 )^{-1}-0.5= \ \](https://tex.z-dn.net/?f=%28+frac%7Ba%5E%7B-1%7D-b%5E%7B-1%7D%7D%7Ba%5E%7B-3%7D%2Bb%5E%7B-3%7D%7D%3A+frac%7Ba%5E2b%5E2%7D%7B%28a%2Bb%29%5E2-3ab%7D%2B1++%29%5E%7B-1%7D-0.5%3D+%5C++%5C+%0A%3D%28+frac%7B+frac%7B1%7D%7Ba%7D-+frac%7B1%7D%7Bb%7D%7D%7B+frac%7B1%7D%7Ba%5E3%7D%2B+frac%7B1%7D%7Bb%5E3%7D++%7D%2A+frac%7Ba%5E2%2B2ab%2Bb%5E2-3ab%7D%7Ba%5E2b%5E2%7D%2B1++%29%5E%7B-1%7D-0.5%3D+%5C++%5C+%0A%3D%28+frac%7B+frac%7Bb-a%7D%7Bab%7D+%7D%7B+frac%7Bb%5E3%2Ba%5E3%7D%7Ba%5E3b%5E3%7D+%7D%2A+frac%7Ba%5E2-ab%2Bb%5E2%7D%7Ba%5E2b%5E2%7D+%2B1+%29%5E%7B-1%7D-0.5%3D+%5C++%5C+%0A%3D%28+frac%7B%28b-a%29a%5E3b%5E3%7D%7Bab%28a%5E3%2Bb%5E3%29%7D%2A+frac%7Ba%5E2-ab%2Bb%5E2%7D%7Ba%5E2b%5E2%7D%2B1++%29%5E%7B-1%7D-0.5%3D+%5C++%5C+%0A%3D%28+frac%7B%28b-a%29%7D%7B%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29%7D%2A+frac%7Ba%5E2-ab%2Bb%5E2%7D%7B1%7D+%2B1+%29%5E%7B-1%7D-0.5%3D+%5C++%5C+%0A)
![=( frac{b-a}{a+b}+1 )^{-1}-0.5=( frac{b-a+a+b}{a+b} )^{-1}-0.5= \ \
=( frac{2b}{a+b} )^{-1}-0.5= frac{a+b}{2b}- frac{1}{2}= frac{a+b-b}{2b}= frac{a}{2b} =( frac{b-a}{a+b}+1 )^{-1}-0.5=( frac{b-a+a+b}{a+b} )^{-1}-0.5= \ \
=( frac{2b}{a+b} )^{-1}-0.5= frac{a+b}{2b}- frac{1}{2}= frac{a+b-b}{2b}= frac{a}{2b}](https://tex.z-dn.net/?f=%3D%28+frac%7Bb-a%7D%7Ba%2Bb%7D%2B1+%29%5E%7B-1%7D-0.5%3D%28+frac%7Bb-a%2Ba%2Bb%7D%7Ba%2Bb%7D+%29%5E%7B-1%7D-0.5%3D+%5C++%5C+%0A%3D%28+frac%7B2b%7D%7Ba%2Bb%7D+%29%5E%7B-1%7D-0.5%3D+frac%7Ba%2Bb%7D%7B2b%7D-+frac%7B1%7D%7B2%7D%3D+frac%7Ba%2Bb-b%7D%7B2b%7D%3D+frac%7Ba%7D%7B2b%7D++++)
7)
![frac{m^{-2}n^{-1}-m^{-1}n^{-2}}{m^{-2}-n^{-2}}- frac{1}{m}(mn^{-1}+2+m^{-1}n)^{-1}= \ \
= frac{ frac{1}{m^2n}- frac{1}{mn^2} }{ frac{1}{m^2}- frac{1}{n^2} }- frac{1}{m}( frac{m}{n} +2+ frac{n}{m} )^{-1} = \ \
= frac{ frac{n-m}{m^2n^2} }{ frac{n^2-m^2}{m^2n^2} }- frac{1}{m}( frac{m^2+2mn+n^2}{mn} )^{-1}= \ \
= frac{n-m}{m^2n^2}* frac{m^2n^2}{(n-m)(n+m)}- frac{1}{m}( frac{(m+n)^2}{mn} )^{-1}= \ \
= frac{1}{m+n} - frac{1}{m}* frac{mn}{(m+n)^2}= frac{m^{-2}n^{-1}-m^{-1}n^{-2}}{m^{-2}-n^{-2}}- frac{1}{m}(mn^{-1}+2+m^{-1}n)^{-1}= \ \
= frac{ frac{1}{m^2n}- frac{1}{mn^2} }{ frac{1}{m^2}- frac{1}{n^2} }- frac{1}{m}( frac{m}{n} +2+ frac{n}{m} )^{-1} = \ \
= frac{ frac{n-m}{m^2n^2} }{ frac{n^2-m^2}{m^2n^2} }- frac{1}{m}( frac{m^2+2mn+n^2}{mn} )^{-1}= \ \
= frac{n-m}{m^2n^2}* frac{m^2n^2}{(n-m)(n+m)}- frac{1}{m}( frac{(m+n)^2}{mn} )^{-1}= \ \
= frac{1}{m+n} - frac{1}{m}* frac{mn}{(m+n)^2}=](https://tex.z-dn.net/?f=+frac%7Bm%5E%7B-2%7Dn%5E%7B-1%7D-m%5E%7B-1%7Dn%5E%7B-2%7D%7D%7Bm%5E%7B-2%7D-n%5E%7B-2%7D%7D-+frac%7B1%7D%7Bm%7D%28mn%5E%7B-1%7D%2B2%2Bm%5E%7B-1%7Dn%29%5E%7B-1%7D%3D+%5C++%5C+%0A%3D+frac%7B+frac%7B1%7D%7Bm%5E2n%7D-+frac%7B1%7D%7Bmn%5E2%7D++%7D%7B+frac%7B1%7D%7Bm%5E2%7D-+frac%7B1%7D%7Bn%5E2%7D++%7D-+frac%7B1%7D%7Bm%7D%28+frac%7Bm%7D%7Bn%7D+%2B2%2B+frac%7Bn%7D%7Bm%7D+%29%5E%7B-1%7D+%3D++%5C++%5C+%0A%3D+frac%7B+frac%7Bn-m%7D%7Bm%5E2n%5E2%7D+%7D%7B+frac%7Bn%5E2-m%5E2%7D%7Bm%5E2n%5E2%7D+%7D-+frac%7B1%7D%7Bm%7D%28+frac%7Bm%5E2%2B2mn%2Bn%5E2%7D%7Bmn%7D+%29%5E%7B-1%7D%3D+%5C++%5C+%0A%3D+frac%7Bn-m%7D%7Bm%5E2n%5E2%7D%2A+frac%7Bm%5E2n%5E2%7D%7B%28n-m%29%28n%2Bm%29%7D-+frac%7B1%7D%7Bm%7D%28+frac%7B%28m%2Bn%29%5E2%7D%7Bmn%7D+%29%5E%7B-1%7D%3D+%5C++%5C+%0A%3D+frac%7B1%7D%7Bm%2Bn%7D+-+frac%7B1%7D%7Bm%7D%2A+frac%7Bmn%7D%7B%28m%2Bn%29%5E2%7D%3D+++++++++++)
![= frac{1}{m+n}- frac{n}{(m+n)^2}= frac{m+n-n}{(m+n)^2}= frac{m}{(m+n)^2}= frac{0.003}{(0.003+0.007)^2}= \ \
= frac{0.003}{0.01^2}= frac{0.003}{0.0001}=30 = frac{1}{m+n}- frac{n}{(m+n)^2}= frac{m+n-n}{(m+n)^2}= frac{m}{(m+n)^2}= frac{0.003}{(0.003+0.007)^2}= \ \
= frac{0.003}{0.01^2}= frac{0.003}{0.0001}=30](https://tex.z-dn.net/?f=%3D+frac%7B1%7D%7Bm%2Bn%7D-+frac%7Bn%7D%7B%28m%2Bn%29%5E2%7D%3D+frac%7Bm%2Bn-n%7D%7B%28m%2Bn%29%5E2%7D%3D+frac%7Bm%7D%7B%28m%2Bn%29%5E2%7D%3D+frac%7B0.003%7D%7B%280.003%2B0.007%29%5E2%7D%3D+%5C++%5C+%0A%3D+frac%7B0.003%7D%7B0.01%5E2%7D%3D+frac%7B0.003%7D%7B0.0001%7D%3D30+++++++)
7)
Вас заинтересует
1 год назад
1 год назад
8 лет назад
9 лет назад