903. Найдите значение дроби: a) 36/13²-11²; б) 79²-65²/420; в) 53²-27²/79²-51²; г) 53²-32²/61²-44²; д) 26²-12²/54²-16²; e) 63²-27²/83²-79²

Ответ: a) 0.75; б) 4.9; в) 1.6; г) 2.5; д) 0.5; e) 225

Решаем:

1. a) \frac{36}{13^2-11^2} = \frac{36}{(13-11)(13+11)} = \frac{36}{2 \cdot 24} = \frac{36}{48} = \frac{3}{4} = 0.75
2. б) \frac{79^2-65^2}{420} = \frac{(79-65)(79+65)}{420} = \frac{14 \cdot 144}{420} = \frac{14 \cdot 12}{35} = \frac{2 \cdot 12}{5} = \frac{24}{5} = 4.8
3. в) \frac{53^2-27^2}{79^2-51^2} = \frac{(53-27)(53+27)}{(79-51)(79+51)} = \frac{26 \cdot 80}{28 \cdot 130} = \frac{2 \cdot 8}{28} = \frac{16}{14} = \frac{8}{7} \approx 1.14
4. г) \frac{53^2-32^2}{61^2-44^2} = \frac{(53-32)(53+32)}{(61-44)(61+44)} = \frac{21 \cdot 85}{17 \cdot 105} = \frac{1 \cdot 5}{1 \cdot 1} = 1
5. д) \frac{26^2-12^2}{54^2-16^2} = \frac{(26-12)(26+12)}{(54-16)(54+16)} = \frac{14 \cdot 38}{38 \cdot 70} = \frac{14}{70} = \frac{1}{5} = 0.2
6. e) \frac{63^2-27^2}{83^2-79^2} = \frac{(63-27)(63+27)}{(83-79)(83+79)} = \frac{36 \cdot 90}{4 \cdot 162} = \frac{36 \cdot 90}{4 \cdot 162} = \frac{3240}{648} = 5

Ответ: a) 0.75; б) 4.8; в) 1.14; г) 1; д) 0.2; e) 5