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Номер 29 гдз 8 класс алгебра Муравин Муравина

Номер 29

 

\begin{equation} 1)\frac{59^{3}-41^{3}}{18}+59\cdot 41= \end{equation} \begin{equation} =10000 \end{equation} \begin{equation} \frac{(59-41)(59^{2}+59\cdot 14+41^{2})}{18}+ \end{equation} \begin{equation} +59\cdot 41= \end{equation} \begin{equation} =\frac{18\cdot (59^{2}+59\cdot 41+41^{2})}{18}+ \end{equation} \begin{equation} +59\cdot 41= \end{equation} = 592 + 59 • 41 + 412 + 59 • 41 =
= 592 + 2 • 59 • 41 + 412 =
= (59 + 41)2 = 1002 = 10000; \begin{equation} 2)(\frac{97^{3}+83^{3}}{180}-97\cdot 83): \end{equation} \begin{equation} :(35^{2}-28^{2})=\frac{4}{9} \end{equation} \begin{equation} 1.\frac{97^{3}+83^{3}}{180}-97\cdot 83= \end{equation} \begin{equation} =\frac{(97+83)(97^{2}-97\cdot 83+83^{2}}{180}- \end{equation} \begin{equation} -97\cdot 83= \end{equation} \begin{equation} =\frac{180\cdot (97^{2}-97\cdot 83+83^{2})}{180}- \end{equation} \begin{equation} -97\cdot 83= \end{equation} = 972 - 97 • 83 + 832 - 97 • 83 =
= 972 - 2 • 97 • 83 + 832 =
= (97 - 83)2 = 142;
2. 352 - 282 = (35 + 28)(35 - 28) =
= 63 • 7 \begin{equation} 3.\frac{14^{2}}{63\cdot 7}=\frac{14\cdot 17}{9\cdot 7\cdot 7}= \end{equation} \begin{equation} =\frac{7^{2}\cdot 2^{2}}{9\cdot 7^{2}}=\frac{4}{9}; \end{equation} 3) 36,52 - 27,52) : \begin{equation} :(\frac{57^{3}+33^{3}}{90}-57\cdot 33)=24 \end{equation} 1. 36,52 - 27,52 =
= (36,5 + 27,5)(36,5 - 27,5) =
= 64 • 9 \begin{equation} 2.\frac{57^{3}+33^{3}}{90}-57\cdot 33= \end{equation} \begin{equation} =\frac{(57+33)(57^{2}-57\cdot 33+33^{2})}{90}- \end{equation} \begin{equation} -57\cdot 33= \end{equation} \begin{equation} =\frac{90\cdot (57^{2}-57\cdot 33+33^{2})}{90}- \end{equation} \begin{equation} -57\cdot 33= \end{equation} = 572 - 57 • 33 + 332 - 57 • 33 =
= 572 - 2 • 57 • 33 + 332 =
= (57 - 33)2 = 24 \begin{equation} 3.\frac{64\cdot 9}{24}=\frac{8\cdot 8\cdot 9}{8\cdot 3}=24; \end{equation} \begin{equation} 4)\frac{77^{3}-69^{3}}{70^{2}-62^{2}}- \end{equation} \begin{equation} -\frac{77^{3}+41^{3}}{125^{2}-49}-\frac{1}{2}=87 \end{equation} \begin{equation} 1.\frac{77^{3}-69^{3}}{70^{2}-62^{2}}= \end{equation} \begin{equation} =\frac{(77-69)(77^{2}+77\cdot 69+69^{2})}{(70+62)(70-62)}= \end{equation} \begin{equation} =\frac{8\cdot (77^{2}+77\cdot 69+69^{2})}{132\cdot 8}= \end{equation} \begin{equation} =\frac{77^{2}+77\cdot 69+69^{2})}{132} \end{equation} \begin{equation} 2.\frac{77^{3}+41^{3}}{125^{2}-49}= \end{equation} \begin{equation} =\frac{(77+41)(77^{2}-77\cdot 41+41^{2})}{(125+7)(125-7)}= \end{equation} \begin{equation} =\frac{1+8\cdot (77^{2}-77\cdot 41+41^{2})}{132\cdot 118}= \end{equation} \begin{equation} =\frac{77^{2}-77\cdot 41+41^{2})}{132} \end{equation} \begin{equation} 3.\frac{77^{2}+77\cdot 69+69^{2})}{132}- \end{equation} \begin{equation} -\frac{77^{2}-77\cdot 41+41^{2})}{132}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{77^{2}+77\cdot 69+69^{2}-77^{2}+}{132} \end{equation} \begin{equation} +\frac{77\cdot 41-41^{2}}{132}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{77\cdot 69+69^{2}+77^{2}\cdot 41-41^{2}}{132}- \end{equation} \begin{equation} -\frac{1}{2}= \end{equation} \begin{equation} =\frac{77\cdot 69+77\cdot 41+69^{2}-41^{2}}{132}- \end{equation} \begin{equation} -\frac{1}{2}= \end{equation} \begin{equation} =\frac{77(69+41)+(69+41)(69-41)}{132}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{77(69+41)+}{132} \end{equation} \begin{equation} +\frac{(69+41)(69-41)}{132}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{77\cdot 110+110\cdot 28}{132}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{110\cdot (77+28)}{132}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{5\cdot 105}{6}-\frac{1}{2}= \end{equation} \begin{equation} =\frac{525-3}{6}=\frac{522}{6}=87. \end{equation}