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\(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}=\frac{31}{1.3}+\frac{31}{3.5}+\frac{31}{5.7}+\frac{31}{7.9}+\frac{31}{9.11}+\frac{31}{11.13}\\ \)
\(=\frac{31}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{31}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{31}{2}.\left(1-\frac{1}{13}\right)=\frac{31}{2}.\frac{12}{13}=\frac{31.6}{13}=\frac{186}{13}\)
\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\Leftrightarrow x=\frac{195}{13}=15\)
\(x-\left(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\)\(\frac{9}{13}\)(1)
Đặt \(A=\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\)
\(A=31\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)
\(\Rightarrow2A=31\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(2A=31\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(2A=31\left(2-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(2A=31\left(2-\frac{1}{13}\right)\)
\(2A=31.\frac{25}{13}\)
\(2A=\frac{775}{13}\)
\(\Rightarrow A=\frac{775}{13}:2\)
\(A=\frac{775}{26}\)
Thay vào (1) ta có:
\(x-\frac{775}{26}=\frac{9}{13}\)
\(\Leftrightarrow x=\frac{9}{13}+\frac{775}{26}\)
\(\Leftrightarrow x=\frac{61}{2}\)
Ta có: x-(\(\frac{31}{5}+\frac{31}{3.5}+\frac{31}{5.7}+\frac{31}{7.9}+\frac{31}{9.11}\)\(+\frac{31}{11.13}\))=\(\frac{9}{13}\)
x-\(\frac{31}{5}\)-\(\frac{31}{2}\)x(\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\))=\(\frac{9}{13}\)
x-\(\frac{31}{5}-\frac{31}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{11}-\frac{1}{13}\right)\)=\(\frac{9}{13}\)
x-\(\frac{31}{5}\)\(-\frac{31}{2}\left(\frac{1}{3}-\frac{1}{13}\right)=\frac{9}{13}\)
x-\(\frac{31}{5}-\frac{31}{2}.\frac{10}{39}\)\(=\frac{9}{13}\)
x-\(\frac{31}{5}-\frac{155}{39}=\frac{9}{13}\)
x-\(\frac{434}{195}\)=\(\frac{9}{13}\)
x =\(\frac{9}{13}+\frac{434}{195}=\frac{569}{195}\)
nhé
(1+1+1+.............+1+1):50+2010-12xX=91
(1x50):50+2010-12xX
50:50+2010-12xX=91
1+2010-12xX=91
2011-12xX=91
12xX=2011-91
12xX=1920
x=1920:12
x=160
a)\(\frac{27}{5}\text{x}\frac{91}{12}\text{x}\frac{125}{9}\text{x}\frac{96}{13}=\frac{27}{9}\text{x}\frac{91}{13}\text{x}\frac{125}{5}\text{x}\frac{96}{12}=3\text{x}7\text{x}25\text{x}8\)
Đến đây tự tính nha !
b)\(\frac{2539}{35}\text{x}\frac{7}{90}+\frac{561}{35}\text{x}\frac{7}{90}=\frac{7}{90}\text{x}\left(\frac{2539}{35}+\frac{561}{35}\right)=\frac{7}{90}\text{x}\frac{3100}{35}=\frac{3100}{90}\text{x}\frac{7}{35}=\frac{310}{9}\text{x}\frac{1}{5}=\frac{62}{9}\)
a. 420 : (x : 39) = 105
x : 39 = 420 : 105
x : 39 = 4
x = 4 x 39
x = 156
b. 200 - 18 : (372 : 3 : x - 1) - 28 = 166
200 - 28 - 166 = 18 : (372 : 3 : x - 1)
6 = 18 : (124 : x - 1)
18 : (124 : x - 1) = 6
124 : x - 1 = 18 : 6
124 : x - 1 = 3
124 : x = 4
x = 124 : 4
x = 31
c. 429 : (x + 31) = 11
x + 31 = 429 : 11
x + 31 = 39
x = 39 - 31
x = 8
d. 1615 : (X x 19) = 17
X x 19 = 1615 : 17
X x 19 = 95
X = 95 : 19
X = 5
cho mình xin tick nhé !
a: 420:(x:39)=105
=>\(x:39=420:105=4\)
=>\(x=4\times39=156\)
b: \(200-18:\left(372:3:x-1\right)-28=166\)
=>\(172-18:\left(124:x-1\right)=166\)
=>\(18:\left(124:x-1\right)=172-166=6\)
=>\(124:x-1=18:6=3\)
=>\(124:x=3+1=4\)
=>\(x=\frac{124}{4}=31\)
c: \(429:\left(x+31\right)=11\)
=>x+31=429:11=39
=>x=39-31=8
d: \(1615:\left(x\times19\right)=17\)
=>\(x\times19=1615:17=95\)
=>x=95:19=5
a) \(\dfrac{25}{37}\times\dfrac{18}{29}+\dfrac{18}{29}\times\dfrac{12}{37}\)
\(=\dfrac{18}{29}\times\left(\dfrac{25}{37}+\dfrac{12}{37}\right)\)
\(=\dfrac{18}{29}\times\dfrac{37}{37}\)
\(=\dfrac{18}{29}\times1\)
\(=\dfrac{18}{29}\)
b) \(\dfrac{31}{85}\times\dfrac{11}{19}+\dfrac{31}{85}\times\dfrac{12}{19}-\dfrac{42}{19}\times\dfrac{31}{85}\)
\(=\dfrac{31}{85}\times\left(\dfrac{11}{19}+\dfrac{12}{19}-\dfrac{42}{19}\right)\)
\(=\dfrac{31}{85}\times\dfrac{-19}{19}\)
\(=\dfrac{31}{85}\times-1\)
\(=-\dfrac{31}{85}\)
c) \(\dfrac{16}{53}:\dfrac{17}{9}-\dfrac{16}{53}:\dfrac{17}{8}\)
\(=\dfrac{16}{53}:\left(\dfrac{9}{17}-\dfrac{8}{17}\right)\)
\(=\dfrac{16}{53}:\dfrac{1}{17}\)
\(=\dfrac{16}{901}\)
c) \(\dfrac{1}{5}\times\dfrac{12}{31}\times\dfrac{4}{3}+\dfrac{19}{31}\times\dfrac{4}{15}\)
\(=\dfrac{4}{15}\times\dfrac{12}{31}+\dfrac{19}{31}\times\dfrac{4}{15}\)
\(=\dfrac{4}{15}\times\left(\dfrac{12}{31}+\dfrac{19}{31}\right)\)
\(=\dfrac{4}{15}\times\dfrac{31}{31}\)
\(=\dfrac{4}{15}\times1\)
\(=\dfrac{4}{15}\)
a: =18/29*(25/37+12/37)
=18/29
b: =31/85(11/19+12/19-42/19)
=-31/85
c; =16/53(9/17+8/17)=16/53
d: =4/15(12/31+19/31)=4/15
#)Giải :
\(200-18:\left(372:3x-1\right)-28=166\)
\(\Leftrightarrow200-18:\left(372:3x-1\right)=194\)
\(\Leftrightarrow18:\left(372:3x-1\right)=6\)
\(\Leftrightarrow372:3x-1=3\)
\(\Leftrightarrow3x-1=124\)
\(\Leftrightarrow3x=125\)
\(\Leftrightarrow x=\frac{125}{3}\)
200 - 18 : (372 : 3 . x - 1) - 28 = 166
=> 200 - 18 : (372 : 3.x - 1) = 166 + 28
=> 200 - 18 : (372 : 3.x) - 1) = 194
=> 18 : (372 : 3.x - 1) = 200 - 194
=> 18 : (372 : 3.x - 1) = 6
=> 372 : 3.x - 1 = 18 : 6
=> 372 : 3.x - 1 = 3
=> 372 : 3.x = 3 + 1
=> 372 : 3.x = 4
=> 3.x = 372 : 4
=> 3.x = 93
=> x = 93 : 3
=> x = 31
#)Next:
\(\left(100-99+98-97+...+2-1\right):50+2010-12x=91\)
\(\Leftrightarrow\left[\left(100-99\right)+\left(98-97\right)+...+\left(2-1\right)\right]:50+2010-12x=91\)
\(\Leftrightarrow\left[1+1+...+1\right]:50+2010-12x=91\)
\(\Leftrightarrow50:50+2010-12x=91\)
\(\Leftrightarrow1+2010-12x=91\)
\(\Leftrightarrow2011-12x=91\)
\(\Leftrightarrow12x=1920\)
\(\Leftrightarrow x=160\)
(100 - 99 + 98 - 97 + 96 - 95 + ... +4- 3 + 2- 1) : 50 + 2010 - 12.x = 91 (50 cặp số hạng có hiệu bằng 1)
=> 1 + 1 + 1 + .... + 1 + 1) : 50 + 2010 - 12. x = 91
=> 50 : 50 + 2010 - 12.x = 91
=> 1 + 2010 - 12.x = 91
=> 2011- 12.x = 91
=> 12.x = 2011 - 91
=> 12.x = 1920
=> x = 1920 : 12
=> x = 160
#)Next :
\(x-\left(\frac{31}{3}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)
\(\Leftrightarrow x-\left[\frac{2}{31}:\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{25}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\right]=\frac{9}{13}\)
\(\Leftrightarrow x-\left[\frac{2}{31}:\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\right]=\frac{9}{13}\)
\(\Leftrightarrow x-\left[\frac{2}{31}:\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\right]=\frac{9}{13}\)
\(\Leftrightarrow x-\left[\frac{2}{31}:\left(1-\frac{1}{13}\right)\right]=\frac{9}{13}\)
\(\Leftrightarrow x-\frac{186}{13}=\frac{9}{13}\)
Đến đây thì ez rùi nhé ^^
x - (31/3 + 31/15 + .... + 31/143) = 9/13
=> x - (31/1.3 + 31.3.5 + ... + 31/11.13) = 9/13
=> x - 31/2.(2/1.3 + 2/3.5 + ... + 2/11.13) = 9/13
=> x - 31/2.(1 - 1/3 + 1/3 - 1/5 + ... + 1/11 - 1/13) = 9/13
=> x - 31/2. (1 - 1/13) = 9/13
=> x - 31/2.12/13 = 9/13
=> x - 186/13 = 9/13
=> x = 186/13 + 9/13
=> x = 15
x - (31/3 + 31/15 + 31/35 + 31/63 + 31/99 + 31/143) = 9/13
<=> x - 186/13 = 9/13
<=> x = 9/13 + 186/13
<=> x = 15
\(200-18:\left(372:3x-1\right)-28=166\)
\(< =>200-18:\left(372:3x-1\right)=194\)
\(< =>18:\left(372:3x-1\right)=6\)
\(< =>372:3x-1=3\)
\(< =>3x-1=124\)
\(< =>3x=125\)
\(=>x=\frac{125}{3}\)
b,c tương tự