Question

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

Answer 1

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

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

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

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

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