Вычислите наиболее рациональным способом:
а) $(\frac{97^3 - 53^3}{44} + 97 * 53) : (152,5^2 - 27,5^2)$;
б) $(36,5^2 - 27,5^2) : (\frac{57^3 + 33^3}{90} - 57 * 33)$;
в) $(\frac{79^3 - 41^3}{38} + 79 * 41) : (133,5^2 - 58,5^2)$;
г) $(94,5^2 - 30,5^2) : (\frac{69^3 + 29^3}{98} - 69 * 29)$.
$(\frac{97^3 - 53^3}{44} + 97 * 53) : (152,5^2 - 27,5^2) = (\frac{(97 - 53)(97^2 + 97 * 53 + 53^2)}{44} + 97 * 53) : ((152,5 - 27,5)(152,5 + 27,5)) = (\frac{44 * (97^2 + 97 * 53 + 53^2)}{44} + 97 * 53) : (125 * 180) = (97^2 + 97 * 53 + 53^2 + 97 * 53) : (125 * 180) = (97^2 + 2 * 97 * 53 + 53^2) : (125 * 180) = (97 + 53)^2 : (125 * 180) = \frac{150^2}{125 * 180} = \frac{150 * 150}{125 * 180} = \frac{6 * 5}{5 * 6} = 1$
$(36,5^2 - 27,5^2) : (\frac{57^3 + 33^3}{90} - 57 * 33) = ((36,5 - 27,5)(36,5 + 27,5)) : (\frac{(57 + 33)(57^2 - 57 * 33 + 33^2)}{90} - 57 * 33) = (9 * 64) : (\frac{90 * (57^2 - 57 * 33 + 33^2)}{90} - 57 * 33) = (9 * 64) : (57^2 - 57 * 33 + 33^2 - 57 * 33) = (9 * 64) : (57^2 - 2 * 57 * 33 + 33^2) = \frac{9 * 64}{(57 - 33)^2} = \frac{9 * 64}{24^2} = \frac{9 * 64}{24 * 24} = \frac{1 * 64}{8 * 8} = 1$
$(\frac{79^3 - 41^3}{38} + 79 * 41) : (133,5^2 - 58,5^2) = (\frac{(79 - 41)(79^2 + 79 * 41 + 41^2)}{38} + 79 * 41) : ((133,5 - 58,5)(133,5 + 58,5)) = (\frac{38 * (79^2 + 79 * 41 + 41^2)}{38} + 79 * 41) : (75 * 192) = (79^2 + 79 * 41 + 41^2 + 79 * 41) : (75 * 192) = \frac{79^2 + 2 * 79 * 41 + 41^2}{75 * 192} = \frac{(79 + 41)^2}{75 * 192} = \frac{120^2}{75 * 192} = \frac{120 * 120}{75 * 192} = \frac{8 * 5}{5 * 8} = 1$
$(94,5^2 - 30,5^2) : (\frac{69^3 + 29^3}{98} - 69 * 29) = ((94,5 - 30,5)(94,5 + 30,5)) : (\frac{(69 + 29)(69^2 - 69 * 29 + 29^2)}{98} - 69 * 29) = (64 * 125) : (\frac{98 * (69^2 - 69 * 29 + 29^2)}{98} - 69 * 29) = (64 * 125) : (69^2 - 69 * 29 + 29^2 - 69 * 29) = \frac{64 * 125}{69^2 - 2 * 69 * 29 + 29^2} = \frac{64 * 125}{(69 - 29)^2} = \frac{64 * 125}{40^2} = \frac{64 * 125}{40 * 40} = \frac{1 * 125}{5 * 5} = 5$
Пожауйста, оцените решение
