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1: 243^5=(3^5)^5=3^25
3*27^8=3*3^24=3^25=243^5
3: 3^300=27^100
2^200=4^100
mà 27>4
nên 3^300>2^200
4: 15^2=3^2*5^2
81^3*125^3=3^12*5^9
=>15^2<81^3*125^3
6: 125^5=5^15
25^7=5^14
mà 15>14
nên 125^5>25^7
Bài 1 :
a) A= (1;2;3;4;5)
b) B= ( 63;64;65;66;67;68;69;70)
Bài 2 :
a) 10x-5 = 11.5-10
10x-5 = 55-10
10x=45+5
10x=50
x=5
b) 27-3x=9.2-3
27-3x = 18-3
27-3x=15
3x=27-15
3x=12
x=4
c) 4x-15=12:12
4x-15=1
4x=16
x=4
d) 2+13x=14.2
13x=28-2
13x=26
x=2
a) \(10x-5=45\)
\(10x=40\)
\(x=4\)
b) \(27-3x=15\)
\(3x=27-15=12\)
\(x=\dfrac{12}{3}=4\)
c) \(4x-15=1\)
\(4x=16\)
\(x=\dfrac{16}{4}=4\)
d) \(2+13x=28\)
\(13x=26\)
\(x=\dfrac{26}{13}=2\)
A = 13/21.2/11 + 13/21.9/11 + 8/21
= (13/21) + (13/21) + (8/21)
= (13 + 13 + 8)/21
= 34/21
B = (1 - 1/5)(1 - 2/5)(1 - 3/5)...(1 - 9/5)
= (4/5)(3/5)(2/5)(1/5)(0/5)(-1/5)(-2/5)(-3/5)(-4/5)
= 0
C = (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/50)
= (1/2)(2/3)(3/4)(4/5)...(49/50)
= 1/50
D = (2^2/1.3) * (3^2/2.4) * (4^2/3.5) * (5^2/4.6) * (6^2/5.7)
= (4/3) * (9/8) * (16/15) * (25/23) * (36/35)
= 0.979
\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{49.50}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}\)
\(=\frac{49}{50}\)
5,có thể bn sai đề chỗ \(\frac{1920}{111.2013}\),phải là \(\frac{1902}{111.2013}\)
\(F=\frac{3}{15.18}+\frac{11}{18.29}+\frac{12}{29.41}+\frac{70}{41.111}+\frac{1902}{111.2013}\)
\(=\frac{18-15}{15.18}+\frac{29-18}{18.29}+\frac{41-29}{12}+\frac{111-41}{41.111}+\frac{2013-111}{1902}\)
\(=\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{29}+\frac{1}{29}-\frac{1}{41}+\frac{1}{41}-\frac{1}{111}+\frac{1}{111}-\frac{1}{2013}\)
\(=\frac{1}{15}-\frac{1}{2013}=\frac{222}{3355}\)