\(\left(\frac{2}{11.13}+\frac{2}{13.15}+.........\frac{2}{19.20}\right)-x+\frac{221}{231}=\frac{4}{3}\)
tìm x, biết
a, \(\left(\frac{11}{12}+\frac{11}{12.23}+\frac{11}{23.24}+...+\frac{11}{89.100}\right)+x=\frac{5}{3}\)
b, \(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
Tìm x:
\((\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21})-x+\frac{221}{231}=\frac{4}{3}\)
a)Tìm số tự nhiên a nhỏ nhất sao cho a chia cho 3, cho 5, cho 7 được số dư thứ tự là 2, 4, 6
b) \(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
c)\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(b.\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Leftrightarrow\frac{35+9}{105}< \frac{x}{210}< \frac{60+63+35}{105}\)
\(\Leftrightarrow\frac{44}{105}< \frac{x}{210}< \frac{158}{105}\)
\(\Leftrightarrow\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)
Suy ra \(x\in\left\{89;90;100;...;313;314;315\right\}\)
\(c.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\frac{1}{11}-\frac{1}{21}-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\frac{21-11-231x+221}{231}=\frac{308}{231}\)
\(\Leftrightarrow-231x=308-21+11-221\)
\(\Leftrightarrow-231x=77\)
\(\Leftrightarrow x=-\frac{77}{231}=-\frac{1}{3}\)
^^
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right).231-\left(3^{16}:3^{14}-2^8:2^6\right).x=2013^0\)
Ta có:
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right).231-\left(3^{16}:3^{14}-2^8:2^6\right).x=2013^0\)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right).231-\left(3^2-2^2\right).x=1\)
\(\left(\frac{1}{11}-\frac{1}{21}\right).231-x=1\)
\(\frac{10}{231}.231-x=1\)
\(10-x=1\)
\(x=9\)
Vậy,.............
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Có 2/11*13 + 2/13*15 + ...........+ 2/19*21
=1/11 - 1/13 + 1/13 - 1/15 + ............. + 1/19 - 1/21 (tính chất của sai phân)
= 1/11 - 1/21
Nên (2/11*13 + 2/13*15+.........+2/19*21)*231
=(1/11 - 1/21) * 231
=1/11 * 231 -1/21 * 231 (tính chất của phân phối)
=21 - 11= 10
và 3^16:3^14 - 2^8:2^6 = 3^2 - 2^2 = 9 - 4 = 5 (tính chất của phép chia 2 lũy thừa cùng cơ số)
Suy ra 10 - 5.x = 2013^0 = 1 (vì x^0 =1)
10 - 5.x = 1
5.x = 10 - 1 = 9 (vô lý vì 5.x chia hết cho 5 mà 9 ko chia hết cho 5)
Vậy, ko có số x thỏa mãn đề bài
tìm x biết:
b)\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+\frac{23}{231}=\frac{5}{77}\)
Đặt \(A=\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\)
\(A=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{19}-\frac{1}{21}\)
\(A=\frac{1}{11}-\frac{1}{21}=\frac{10}{231}\)
thay A vào ta được:
\(\frac{10}{231}-x+\frac{23}{231}=\frac{5}{77}\)
\(x+\frac{23}{231}=\frac{10}{231}-\frac{5}{77}=-\frac{5}{231}\)
\(x=-\frac{5}{231}-\frac{23}{231}=\frac{-4}{33}\)
\(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}-x+\frac{23}{231}=\frac{5}{77}\)\(\frac{5}{77}\)
=>\(\frac{1}{11}-\frac{1}{21}-x+\frac{23}{231}=\frac{5}{77}\)
=>\(\frac{10}{231}+\frac{23}{231}-x=\frac{5}{77}\)
=>\(\frac{33}{231}-x=\frac{5}{77}\)
=>\(\frac{1}{7}-x=\frac{5}{77}\)
=>\(\frac{11}{77}-x=\frac{5}{77}\)
=>\(x=\frac{11}{77}-\frac{5}{77}=\frac{6}{77}\)
Vậy \(x=\frac{6}{77}\)
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right).462-x=19\)
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\) ) . 462 - x = 19
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\) . 462 - x = 19
\(\left(\frac{1}{11}-\frac{1}{21}\right)\) . 462 - x = 19
... Chúc bạn học tốt !
\(\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+\frac{2}{15\cdot17}+\frac{2}{17\cdot19}+\frac{2}{19\cdot21}\right)\)\(\cdot462-x=19\)
\(\left(\frac{1}{11\cdot13}+\frac{1}{13\cdot15}+\frac{1}{15\cdot17}+\frac{1}{17\cdot19}+\frac{1}{19\cdot21}\right)\)\(\cdot462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\)\(\cdot462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)
\(\frac{10}{231}\cdot462-x=19\)
\(20-x=19\)
\(x=20-19\)
\(x=1\)
tìm x biết
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right).462-\left[0,04:\left(x+1,05\right)\right]\)
bạn nguyệt hằng giải sai rồi 1,5 chứ ko phải 15
Tìm x biết \(\frac{2}{11.13}+\frac{2}{13.15}+....+\frac{2}{19.21}.x+\frac{23}{231}=\frac{5}{77}\)
2/11.13+2/13.15+...+2/19.21x+23/231=5/77
1/11-1/13+1/13-1/15+...+1/19-1/21x+23/231=5/77
1/11+(-1/13+1/13)+(-1/15+1/15)+...+(-1/19+1/19)-1/21x+23/231=5/77
1/11+0+0+0+...+0-1/21x+23/231=5/77
1/11-1/21x+23/231=5/77
21/231-11/231x+23/231=5/77
10/231x+23/231=5/77
10/231x =5/77-23/231
10/231x =15/231-23/231
10/231x =(-8)/231
x =-8/231:10/231
x =-4/5
vậy x=-4/5
ở trên mình tính lộn.nhớ ****
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+..............\frac{2}{19.21}\right).462-\frac{17}{x+1.05}=19\)
Tìm x
\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right).462-\frac{17}{x+1,05}=19.\)
\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{21}\right)462-\frac{17}{x+1,05}=19\)
\(\Leftrightarrow20-\frac{17}{x+1,05}=19\)
\(\Leftrightarrow1-\frac{17}{x+1,05}=0\)
\(\Leftrightarrow x+1,05=17\)
\(\Leftrightarrow x=15,95\)