2/2*3-2/3*5-...-2/25*27-2/27
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NV
1
13 tháng 8 2017
\(\dfrac{-2}{1.3}-\dfrac{2}{3.5}-\dfrac{2}{5.7}-...-\dfrac{2}{19.21}-\dfrac{2}{21.23}-\dfrac{2}{23.25}-\dfrac{2}{25.27}-\dfrac{1}{27}\)\(=\dfrac{-2}{1.3}+\dfrac{-2}{3.5}+\dfrac{-2}{5.7}+...+\dfrac{-2}{19.21}+\dfrac{-2}{21.23}+\dfrac{-2}{23.25}+-\dfrac{2}{25.27}-\dfrac{1}{27}\)Đặt:
\(A=\dfrac{-2}{1.3}+\dfrac{-2}{3.5}+\dfrac{-2}{5.7}+...+\dfrac{-2}{19.21}+\dfrac{-2}{21.23}+\dfrac{-2}{23.25}+\dfrac{-2}{25.27}\)\(A=-1\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{25}-\dfrac{1}{27}\right)\)
\(A=-1\left(1-\dfrac{1}{27}\right)\)
\(A=-1.\dfrac{26}{27}=-\dfrac{26}{27}\)
Thay vào biểu thức ban đầu ta có:
Giá trị là:
\(-\dfrac{26}{27}-\dfrac{1}{27}=-\dfrac{27}{27}=-1\)
BJ
4
T
10 tháng 9 2023
\(a,\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot\left(3^3\right)^7}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}\)
\(=\dfrac{5^{16}\cdot3^{21}}{5^{15}\cdot3^{22}}=\dfrac{5}{3}\)
\(b,\left(-0,2\right)^2\cdot5-\dfrac{2^{13}\cdot27^3}{4^6\cdot9^5}\)
\(=0,04\cdot5-\dfrac{2^{13}\cdot\left(3^3\right)^3}{\left(2^2\right)^6\cdot\left(3^2\right)^5}\)
\(=0,2-\dfrac{2^{13}\cdot3^9}{2^{12}\cdot3^{10}}\)
\(=0,2-\dfrac{2}{3}\)
\(=-\dfrac{7}{15}\)
\(c,\dfrac{5^6+2^2\cdot25^3+2^3\cdot125^2}{26\cdot5^6}\)
\(=\dfrac{5^6+2^2\cdot\left(5^2\right)^3+2^3\cdot\left(5^3\right)^2}{5^6\cdot26}\)
\(=\dfrac{5^6+4\cdot5^6+8\cdot5^6}{5^6\cdot26}\)
\(=\dfrac{5^6\left(1+4+8\right)}{5^6\cdot26}\)
\(=\dfrac{13}{26}\)
\(=\dfrac{1}{2}\)
#\(Toru\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
10 tháng 9 2023
\(a,\dfrac{5^{16}.27^7}{125^5.9^{11}}=\dfrac{\left(5^2\right)^8.9^7.3^7}{25^5.5^5.9^{11}}\\ =\dfrac{25^8.9^7.\left(3^2\right)^3.3}{25^5.\left(5^2\right)^2.5.9^{11}}=\dfrac{25^8.9^7.9^3.3}{25^5.25^2.5.9^{11}}\\ =\dfrac{25^8.9^{10}.3}{25^7.5.9^{11}}=\dfrac{25^7.9^{10}.25.3}{25^7.9^{10}.5.9}\\ =\dfrac{25.3}{5.9}=\dfrac{5.5.3}{5.3.3}=\dfrac{5}{3}\)
MN
9 tháng 1 2016
10) 37.(27+25)-27.(37+25)=37.27+37.25-27.37-27.25
=37.25-27.25=25(37-27)=25.10=250
11)3.(-5+3)+7(2+5)=3.(-2)+7.7=-6+49=43
12)-3.(2-7)-6(8-5)=-3.(-5)-6.3=15-18=-3
C
6 tháng 4 2022
2/25=.2../25 .27../36=3/4
3/.12..=9/36
15/27=5/..9..
..20..28=5/7
36/72=..1../2
6 tháng 4 2022
\(\dfrac{2}{25}=\dfrac{2}{25}\)
\(\dfrac{27}{36}=\dfrac{3}{4}\)
\(\dfrac{3}{12}=\dfrac{9}{36}\)
\(\dfrac{15}{27}=\dfrac{5}{9}\)
\(\dfrac{20}{28}=\dfrac{5}{7}\)
\(\dfrac{36}{72}=\dfrac{1}{2}\)
20 tháng 12 2021
a: \(=3\sqrt{3}-2\sqrt{3}+4\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)
20 tháng 5 2018
a) \(2^x-15=17\)
\(2^x=17+15\)
\(2^x=32\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
b) \(27.3^x=243\)
\(3^x=243:27\)
\(3^x=9\)
\(\Rightarrow3^x=3^2\)
\(\Rightarrow x=2\)
c) \(3^x+25=26.2^2+2.3^0\)
\(3^x+25=104+2\)
\(3^x+25=106\)
\(3^x=106-25\)
\(3^x=81\)
\(\Rightarrow3^x=3^4\)
\(\Rightarrow x=4\)
d) \(\left(7x-11\right)^3=2^5.5^2+200\)
\(\left(7x-11\right)^3=800+200\)
\(\left(7x-11\right)^3=1000\)
\(\Rightarrow\left(7x-11\right)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(7x=10+11\)
\(7x=21\)
\(x=21:7\)
\(x=3\)
e) \(3^x.3=27\)
\(3^x=27:3\)
\(3^x=9\)
\(\Rightarrow3^x=3^2\)
\(\Rightarrow x=2\)
20 tháng 5 2018
a) \(2^x-15=17\)
\(\Leftrightarrow2^x=17+15\)
\(\Leftrightarrow2^x=32\)
\(\Leftrightarrow2^x=2^5\)
\(\Leftrightarrow x=5\)
Vậy x = 5
b) \(27.3^x=243\)
\(\Leftrightarrow3^x=243:27\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Leftrightarrow x=2\)
Vậy x = 2
c) \(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=800+200\)
\(\Leftrightarrow\left(7x-11\right)^3=1000\)
\(\Leftrightarrow\left(7x-11\right)^3=10^3\)
\(\Leftrightarrow7x-11=10\)
\(\Leftrightarrow7x=10+11\)
\(\Leftrightarrow7x=21\)
\(\Leftrightarrow x=21:7\)
\(\Leftrightarrow x=3\)
Vậy x = 3
d) \(3^x.3=27\)
\(\Leftrightarrow3^x=27:3\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Leftrightarrow x=2\)
Vậy x = 2
_Chúc bạn học tốt_
LT
Tìm x biết
a) (x-1/2)^2=4
b) 10/1/2-(x+1/3)^2=1/1/2
c) (x-1/5)^2+17/25=26/25
d) 1/5/27+(3x-7/9)^3=24/27
1
11 tháng 7 2019
a) (x - 1/2)2 = 4
<=> (x - 1/2)2 = 22
<=> x - 1/2 = -2; 2
<=> x - 1/2 = 2 hoặc x - 1/2 = -2
x = 2 + 1/2 x = -2 + 1/2
x = 5/2 x = -3/2
=> x = 5/2 hoặc x = -3/2
b) 10/1/2 - (x + 1/3)2 = 1/1/2
<=> -(x + 1/3)2 = 1/1/2 - 10/1/2
<=> -(x + 1/3)2 = 1/2 - 5
<=> -(x + 1/3)2 = -5.2 + 1/2
<=> -(x + 1/3)2 = -9/2
<=> (x + 1/3)2 = 9/2
<=> x + 1/3 = \(\sqrt{\frac{9}{2}}\) hoặc x + 1/3 = \(-\sqrt{\frac{9}{2}}\)
x = \(\frac{3\sqrt{2}}{2}\) - 1/3 x = \(-\frac{3\sqrt{2}}{2}\) -1/3
=> x = \(\frac{3\sqrt{2}}{2}\) - 1/3 hoặc x = \(-\frac{3\sqrt{2}}{2}\) -1/3
c) (x - 1/5)2 + 17/25 = 26/25
<=> (x - 1/5)2 = 26/25 - 17/25
<=> (x - 1/5)2 = (3/5)2
<=> x - 1/5 = -3/5; 3/5
<=> x - 1/5 = 3/5 hoặc x - 1/5 = -3/5
x = 3/5 + 1/5 x = -3/5 + 1/5
x = 4/5 x = -2/5
=> x = 4/5 hoặc x = -2/5
kết quả bài này = 1/2