Question

Первому 50 баллов, (номер 354) пожалуйста найдите значение выражения:

Answer 1

$1) \: \frac{ {13}^{2} - {11}^{2} }{36} = \frac{ (13 + 11)(13 - 11)}{36} = \\ = \frac{24 \times 2}{36} = \frac{4}{3} = 1 \frac{1}{3}$
$2) \: \frac{ {53}^{2} - {32}^{2} }{ {61}^{2} - {44}^{2} } = \frac{ (53 + 32)(53 - 32)}{(61 + 44)(61 - 44)} = \\ = \frac{85 \times 21}{105 \times 17} = \frac{5 \times 1}{5 \times 1} = 1$

$3) \: \frac{ {79}^{2} - {65}^{2} }{420} = \frac{ (79+ 65)(79 - 65)}{420} = \\ = \frac{144 \times 14}{420} = \frac{144}{30} = \frac{24}{5} = 4 \frac{4}{5}$

$4) \: \frac{ {26}^{2} - {12}^{2} }{ {54}^{2} - {16}^{2} } = \frac{ (26+12)(26 - 12)}{(54 +16)(54 - 16) } = \\ = \frac{38 \times 14}{70 \times 38} = \frac{1}{5}$

$5) \: \frac{ {53}^{2} - {27}^{2} }{ {79}^{2} - {51}^{2} } = \frac{ (53 + 27)(53 - 27)}{(79 + 51)(79 - 51)} = \\ = \frac{80 \times 26}{130 \times 28} = \frac{20}{5 \times 7} = \frac{4}{7}$

$6) \: \frac{ {63}^{2} - {27}^{2} }{ {83}^{2} - {79}^{2} } = \frac{ (63 + 27)(63 - 27)}{(83 + 79)(83 - 79)} = \\ = \frac{90 \times 36}{162 \times 4} = \frac{10 \times 9}{18} = 5$