a )294 -(7x -217) = 3^8 . 3^11 : 3^11 + 6
b) (3x - 4 ) ^3 = 125
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(\(\dfrac{2}{3}\) - \(\dfrac{11}{7}\) + \(\dfrac{13}{5}\)) - (5 - \(\dfrac{4}{7}\) + \(\dfrac{6}{5}\)) - (\(\dfrac{11}{3}\) - \(\dfrac{3}{5}\))
= \(\dfrac{2}{3}\) - \(\dfrac{11}{7}\) + \(\dfrac{13}{5}\) - 5 + \(\dfrac{4}{7}\) - \(\dfrac{6}{5}\) - \(\dfrac{11}{3}\) + \(\dfrac{3}{5}\)
= (\(\dfrac{2}{3}\) - \(\dfrac{11}{3}\)) - (\(\dfrac{11}{7}\) - \(\dfrac{4}{7}\)) + (\(\dfrac{13}{5}\) - \(\dfrac{6}{5}\)+ \(\dfrac{3}{5}\))
= \(\dfrac{-9}{3}\) - \(\dfrac{7}{7}\) + (\(\dfrac{7}{5}\) + \(\dfrac{3}{5}\)) - 5
= - 3 - 1 + 2 - 5
= - (3 + 1) - ( 5 - 2)
= - 4 - 3
= - 7
a, 11 + 112 + 113 + ... + 117 + 118
= (11 + 112) + (113 + 114) + ... + (117 + 118)
= 11(1 + 11) + 113(1 + 11) + ... + 117(1 + 11)
= 11.12 + 113.12 + .... + 117.12
= 12(11 + 113 + ... + 117) chia hết cho 12
b, 7 + 72 + 73 + 74
= (7 + 73) + (72 + 74)
= 7(1 + 72) + 72(1 + 72)
= 7.50 + 72.50
= 50(7 + 72) chia hết cho 50
c, 3 + 32 + 33 + 34 + 35 + 36
= (3 + 32 + 33) + (34 + 35 + 36)
= 3(1 + 3 + 32) + 34(1 + 3 + 32)
= 3.13 + 34.13
= 13(3 + 34) chia hết cho 13
Bài 1:
ta có: A = 11^9+11^8+..+11+1
=> 11A = 11^10+11^9+...+11^2+11
=> 11A-A = 11^10-1
10A = 11^10 -1
mà (11^10)-1 = (...1) - 1 = (...0) chia hết cho 10
=> A = (11^10-1):10 sẽ chia hết
=> A chia hết cho 5
Bài 2:
ta
Điền dấu <;>;= :
a)11/25..<.......12/25
b)9/5......>.....8/5
c)36/45....=........4/5
d)5/8......<.......3/4
a) 294 - ( 7x - 217 ) = 38 . 311 : 311 + 6
294 - ( 7x - 217 ) = 38 . ( 311 : 311 ) + 6
294 - ( 7x - 217 ) = 38 . 1 + 6
294 - ( 7x - 217 ) = 6561 . 1 + 6
294 - ( 7x - 217 ) = 6561 + 6
294 - ( 7x - 217 ) = 6567
( 7x - 217 ) = 294 - 6567
( 7x - 217 ) = - 6273
7x = - 6273 + 217
7x = - 6056
x = - 6056 : 7
x = - 865,1428571
Vậy x = - 865,1428571
b) ( 3x - 4 )3 = 125
( 3x - 4 )3 = 53
( 3x - 4 ) = 5
3x = 5 + 4
3x = 9
x = 9 : 3
x = 3
Vậy x = 3