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Bài 1 : \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right]:5\times x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \left[\frac{1}{6}+\frac{1}{24}+\frac{2}{15}+\frac{3}{40}\right]:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{5}{12}:5\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{1}{12}\cdot x< \frac{5}{6}\)
=> \(\frac{2}{3}< \frac{x}{12}< \frac{5}{6}\)
=> \(\frac{8}{12}< \frac{x}{12}< \frac{10}{12}\)
=> x = 9
Bài 2 : \(\frac{\left[\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right]}{x}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
=> \(\frac{\left[1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}\right]}{x}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{11\cdot12}\)
=> \(\frac{\left[1-\frac{1}{16}\right]}{x}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=1-\frac{1}{12}\)
=> \(\frac{15}{\frac{16}{x}}=\frac{11}{12}\)
=> \(\frac{15}{16}:x=\frac{11}{12}\)
=> \(x=\frac{45}{44}\)
Bài 3 : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\times(x+1):2}=\frac{399}{400}\)
=> \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\times(x+1)}=\frac{399}{400}\)
=> \(2\left[\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(2\left[\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\times(x+1)}\right]=\frac{399}{400}\)
=> \(\left[\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}\right]=\frac{399}{800}\)
=> \(\frac{1}{2}-\frac{1}{x+1}=\frac{399}{800}\)
=> \(\frac{1}{x+1}=\frac{1}{800}\)
=> x = 799
Bài 2 :
\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right):x=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\) (*)
Ta có : \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}=\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}=\frac{8+4+2+1}{16}=\frac{15}{16}\) (1)
Lại có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(=1\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+...+\left(-\frac{1}{11}+\frac{1}{11}\right)-\frac{1}{12}\)
\(=1-\frac{1}{12}=\frac{11}{12}\) (2)
Thay (1) và (2) vào biểu thức (*) ta được :
\(\frac{15}{16}:x=\frac{11}{12}\)
\(\Leftrightarrow x=\frac{15}{16}:\frac{11}{12}\)
\(\Leftrightarrow x=\frac{45}{44}\)
Vậy : \(x=\frac{45}{44}\)
#)Giải :
11 x ( y - 6 ) = ( 4 x y ) + 11
11 x y - 66 = 44 x y + 11
y x ( 11 + 11 ) = 66 + 44
y x 22 = 110
y = 110 : 22
y = 5
#) Coi như là làm lại đi ha :D
#~Will~be~Pens~#
a 9/15 x y = (5/7 +3/14) x 4/7
9/15 x y = 13/14 x 4/7
9/15 x y = 26/49
y= 26/49 : 9/15
y= 130/147
b, y : 0,25 = (2,5-1,3) : 0,75
y : 1/4 = 8/5
y= 8/5 x 1/4 = 2/5
a/
9/14 x y = (5/7 + 3/14) x 4/7
9/14 x y = 13/14 x 4/7
9/14 x y = 26/49
y = 26/49 : 9/14
y = 52/63
b/
y : 0,25= (2,5 - 1,3) : 0,75
y : 0,25= 1,2 : 0,75
y : 0,25= 1,6
y = 1,6 x 0,25
y = 0,4
chúc học tốt nhé!!! học giỏi !!!
- Ta có: \(\frac{3}{x}+\frac{y}{3}=\frac{5}{6}\)
\(\Leftrightarrow\frac{3}{x}=\frac{5}{6}-\frac{y}{3}\)
\(\Leftrightarrow\frac{3}{x}=\frac{5-2y}{6}\)
\(\Leftrightarrow x.\left(5-2y\right)=18=1.18=\left(-1\right).\left(-18\right)=2.9=\left(-2\right).\left(-9\right)=3.6=\left(-3\right).\left(-6\right)\)
- Vì \(5-2y\)là lẻ \(\Rightarrow\)\(5-2y\in\left\{-9,-3,-1,1,3,9,\right\}\)
- Ta có bảng giá trị:
| \(5-2y\) | \(-9\) | \(-3\) | \(-1\) | \(1\) | \(3\) | \(9\) |
| \(x\) | \(-2\) | \(-6\) | \(-18\) | \(18\) | \(6\) | \(2\) |
| \(y\) | \(7\) | \(4\) | \(3\) | \(2\) | \(1\) | \(-2\) |
| \(\left(TM\right)\) | \(\left(TM\right)\) | \(\left(TM\right)\) | \(\left(L\right)\) | \(\left(L\right)\) | \(\left(L\right)\) |
Vậy \(\left(x,y\right)\in\left\{\left(-2,7\right);\left(-6,4\right);\left(-18,3\right)\right\}\)
!@#$!@$! ^_^ Chúc bn hok tốt ^_^ @#$!#$!
\(3,2:y=16:10\)
\(\dfrac{16}{5}:y=\dfrac{8}{5}\)
\(y=\dfrac{16}{5}:\dfrac{8}{5}\)
\(y=2\)
3,2:y=16:103,2:y=16:10
165:y=85165:y=85
y=165:85y=165:85
y=2.
mình đồng ý với cách làm của bạn Nguyễn Ngọc Huy Toàn