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Đặt tổng trên là A ta có
\(3A=4.5.3+5.6.3+6.7.3+...+30.31.3\)
\(3A=4.5.\left(6-3\right)+5.6.\left(7-4\right)+6.7.\left(8-5\right)+...+30.31.\left(32-29\right)\)
\(3A=4.5.6-3.4.5+5.6.7-4.5.6+6.7.8-5.6.7+...+30.31.32-29.30.31\)
\(3A=30.31.32-3.4.5\Rightarrow A=10.31.32-4.5=9900\)
a, (10/3:x).(-5/4)=-10/3
10/3:x=-10/3:(-5/4)
10/3:x=8/3
x=10/3:8/3
x=5/4
b,(-6/5+x):(-18/5)=-1/4
-6/5+x=-1/4.(-18/5)
-6/5+x=9/10
x=9/10-(-6/5)=9/10+6/5
x=21/10
c,-22/15.x+1/3=-2/5
-22/15.x=-2/5-1/3=-11/15
x=-11/15:(-22/15)
x=11/21
d,(0,25-30%x).1/3=-31/6+1/4=-59/12
1/4-3/10x=-59/12:1/3=-59/4
3/10x=1/4-(-59/4)=1/4+59/4=15
x=15:3/10
x=50
e,(0,5x-3/7):1/2=8/7
1/2x=8/7.1/2=4/7
x=4/7:1/2
x=8/7
a, 2 x 31 x 12 + 4 x 6 x 42 + 8 x 27 x 3
= 2 x 12 x 31 + 4 x 6 x 42 + 8 x 3 x 27
= 24 x 31 + 24 x 42 + 24 x 27
= 24 x ( 31 + 24 + 27 )
= 24 x 82
= 1968
b, 2 x 53 x 12 + 4 x 6 x 87 - 3 x 8 x 40
= 24 x 53 + 24 x 87 - 24 x 40
= 24 x ( 53 + 87 - 40 )
= 24 x 100
= 2400
c, Tương tự
a, 410. 230=220.230=250
b,925.274.813= 350.312.312=374
Tương tự các câu khác....
a, 410.230 = (22)10.230 = 220.230 = 250
b, 925.274.813 = (32)25.(33)4.(34)3 = 350.312.312 = 374
c, 2550.1255 = (52)50.(53)5 = 5100.515 = 5115
d, 643.48.164 = (26)3.(22)8.(24)4 = 218.216.216 = 250
e, 38 : 36 = 32
210 : 83 = 210 : (23)3 = 210 : 29 = 2
127 : 67 = (12 : 6)7 = 27
@Dương Tuyết Mai
\(\left(\frac{17}{28}+18.29+\frac{19}{30}+\frac{30}{31}\right).\left(\frac{-5}{12}+\frac{1}{4}+\frac{1}{6}\right)\)
\(=\left(\frac{17}{28}+18.29+\frac{19}{30}+\frac{30}{31}\right).\left(\frac{-5}{12}+\frac{3}{12}+\frac{2}{12}\right)\)
\(=\left(\frac{17}{28}+18.29+\frac{19}{30}+\frac{30}{31}\right).\left(\frac{-2}{12}+\frac{2}{12}\right)\)
\(=\left(\frac{17}{28}+18.29+\frac{19}{30}+\frac{30}{31}\right).0\)
\(=0\)
A = 4.5 + 5.6 + 6.7 + ... + 30.31
3A = 3.4.5 + 3.5.6 + 3.6.7 + ... + 3.30.31
= (6 - 3).4.5 + (7 - 4).5.6 + (8 - 5).6.7 + ... + (32 - 29).30.31
= 4.5.6 - 3.4.5 + 5.6.7 - 4.5.6 + 6.7.8 - 5.6.7 + ... + 30.31.32 - 29.30.31
= (4.5.6 + 5.6.7 + 6.7.8 + ... + 30.31.32) - (3.4.5 + 4.5.6 + 5.6.7 + ... + 29.30.31)
= 30.31.32 - 3.4.5 = 29760 - 60 = 29700
A = 29700 : 3 = 9900