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rsleptsov
@rsleptsov
August 2022
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вычислите рациональным способом: 45*52-52*42+42*51-51*39+39*50-50*36+36*49-49*33
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PeE4eNkA
1) 45·52 - 52·42 + 42·51 - 51·39 + 39·50 - 50·36 + 36·49 - 49·33 =
= 52(45 - 42) + 51(42 - 39) + 50(39 -36) + 49(36 - 33) =
= 52·3 + 51·3 + 50·3 + 49·3 =
= 3(52 + 51 + 50 + 49) = 3((52 + 50) + (51 + 49)) = 3(102 + 100) = 3·202 = <b>606</b>
2) 9,3·2,5 - 2,5·8,9 + 8,9·2,4 - 2,4·8,5 + 8,5·2,3 - 2,3·8,1 + 8,1·2,2 - 2,2·7,7 =
= 2,5(9,3 - 8,9) + 2,4(8,9 - 8,5) + 2,3(8,5 - 8,1) + 2,2(8,1 - 7,7) =
= 0,4(2,5 + 2,4 + 2,3 + 2,2) = 0,4(2,5 + 2,4 + 4,5) = 0,4(7 + 2,4) =
= 0,4·9,4 = <b>3,76</b>
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Answers & Comments
= 52(45 - 42) + 51(42 - 39) + 50(39 -36) + 49(36 - 33) =
= 52·3 + 51·3 + 50·3 + 49·3 =
= 3(52 + 51 + 50 + 49) = 3((52 + 50) + (51 + 49)) = 3(102 + 100) = 3·202 = <b>606</b>
2) 9,3·2,5 - 2,5·8,9 + 8,9·2,4 - 2,4·8,5 + 8,5·2,3 - 2,3·8,1 + 8,1·2,2 - 2,2·7,7 =
= 2,5(9,3 - 8,9) + 2,4(8,9 - 8,5) + 2,3(8,5 - 8,1) + 2,2(8,1 - 7,7) =
= 0,4(2,5 + 2,4 + 2,3 + 2,2) = 0,4(2,5 + 2,4 + 4,5) = 0,4(7 + 2,4) =
= 0,4·9,4 = <b>3,76</b>