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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{Ta có: }\) \(\frac{1}{4}x+\frac{1}{8}x+\frac{1}{16}x=1\)
\(\Rightarrow\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)x=1\)
\(\Rightarrow\frac{7}{16}x=1\)
\(\Rightarrow x=1:\frac{7}{16}\)
\(\Rightarrow x=\frac{16}{7}\)
Tìm x :
a, 1/4 * x + 1/8 * x + 1/16 * x = 1
x * ( 1/4 + 1/8 + 1/16 ) = 1
x * 7/16 = 1
x = 1 : 7/16
x = 16/7
b, 1/5 + 1/3 x ( x + 1 ) = 1/4
1/3 x ( x + 1 ) = 1/4 - 1/5
1/3 x ( x + 1 ) = 1/20
x + 1 = 1/20 : 1/3
x + 1 = 3/20
x = 1 - 3/20
x = 7/20
Tính nhanh :
1/5 x 27 + 1/5 x 33 + 1/5 x 40
= 1/5 x ( 27 + 33 + 40 )
= 1/5 x 100
= 20
![](https://rs.olm.vn/images/avt/0.png?1311)
= 1/2+ (1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)
= 1/2 -1/100
= 49/100
ko chắc chắn, đúng k mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
bài 2
1,35-x=-16-(-7)
35-x=-9
x=35-(-9)=44
2,/x-2/=9 suy ra x-2=9 hoặc =-9 rồi tự tính
3, suy ra 4-2x=0 hoặc x-3 =0 tụ tính x
4, (x-2)^2=64 = 8^2 suy ra x-2 =8 hoặc -8
Bài 2: Thực hiện phép tính (tính bằng cách hợp lí nếu có thể)
-16 - (35 - x) = -7
-16 - 35 + x = -7
-51 + x = -7
x = -7 - (-51)
x = 44
lx - 2l = 9
=> \(\orbr{\begin{cases}x-2=9\\x-2=-9\end{cases}}\)
=> \(\orbr{\begin{cases}x=9+2\\x=-9+2\end{cases}}\)
=> \(\orbr{\begin{cases}x=11\\x=-7\end{cases}}\)
(4 - 2x) . (x - 3) = 0
=> \(\orbr{\begin{cases}4-2x=0\\x-3=0\end{cases}}\)
=> \(\orbr{\begin{cases}2x=4-0\\x=0+3\end{cases}}\)
=> \(\orbr{\begin{cases}2x=4\\x=3\end{cases}}\)
=> \(\orbr{\begin{cases}x=4\div2\\x=3\end{cases}}\)
=> \(\orbr{\begin{cases}x=2\\x=3\end{cases}}\)
(x - 2)2 - 64 = 0
=> (x - 2)2 = 0 + 64
=> (x - 2)2 = 64
=> (x - 2)2 = 82
=> x - 2 = 8
=> x = 8 + 2
=> x = 10
![](https://rs.olm.vn/images/avt/0.png?1311)
⇒
⇒
*Cách phân tích:
Ta nhận thấy:
Tương tự đến hết dãy
Thay tổng đó vào
*Lưu ý: Nếu tử số không bằng 2 số ở mẫu trừ cho nhau thì phải nhân thêm vào học chia đi
Ví dụ:
1 khác 5-3
Khi đó phải nhân thêm 2/2 vào
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : 1x2x3x...x9-1x2x3x...x8-1x2x3x...x8^2
=1x2x3x...x8x(9-1-8)
=1x2x3x...x8x0
=0
Nhớ k cho mik nha !!!
![](https://rs.olm.vn/images/avt/0.png?1311)
`5`
`a, -7/21 +(1+1/3)`
`=-7/21 + ( 3/3 + 1/3)`
`=-7/21+ 4/3`
`=-7/21+ 28/21`
`= 21/21`
`=1`
`b, 2/15 + ( 5/9 + (-6)/9)`
`= 2/15 + (-1/9)`
`= 1/45`
`c, (9-1/5+3/12) +(-3/4)`
`= ( 45/5-1/5 + 3/12)+(-3/4)`
`= ( 44/5 + 3/12)+(-3/4)`
`= 9,05 +(-0,75)`
`=8,3`
`6`
`x+7/8 =13/12`
`=>x= 13/12 -7/8`
`=>x=5/24`
`-------`
`-(-6)/12 -x=9/48`
`=> 6/12 -x=9/48`
`=>x= 6/12-9/48`
`=>x=5/16`
`---------`
`x+4/6 =5/25 -(-7)/15`
`=>x+4/6 =1/5 + 7/15`
`=> x+ 4/6=10/15`
`=>x=10/15 -4/6`
`=>x=0`
`----------`
`x+4/5 = 6/20 -(-7)/3`
`=>x+4/5 = 6/20 +7/3`
`=>x+4/5 = 79/30`
`=>x=79/30 -4/5`
`=>x= 79/30-24/30`
`=>x= 55/30`
`=>x= 11/6`
\(5)\)
\(A=\dfrac{-7}{21}+\left(1+\dfrac{1}{3}\right)\)
\(A=\dfrac{-7}{21}+\dfrac{4}{3}\)
\(A=\dfrac{-7}{21}+\dfrac{28}{21}\)
\(A=1\)
\(--------------\)
\(B=\dfrac{2}{15}+\left(\dfrac{5}{9}+\dfrac{-6}{9}\right)\)
\(B=\dfrac{2}{15}+\dfrac{-1}{9}\)
\(B=\dfrac{18}{135}+\dfrac{-15}{135}\)
\(B=\dfrac{1}{45}\)
\(------------\)
\(C=9-\dfrac{1}{5}+\dfrac{3}{12}+\dfrac{-3}{4}\)
\(C=\dfrac{44}{5}+\dfrac{3}{12}+\dfrac{-3}{4}\)
\(C=\dfrac{528}{60}+\dfrac{15}{60}+\dfrac{-3}{4}\)
\(C=\dfrac{181}{20}+\dfrac{-3}{4}\)
\(C=\dfrac{181}{20}+\dfrac{-15}{20}\)
\(C=\dfrac{83}{10}\)
\(6)\)
\(a)\) \(x+\dfrac{7}{8}=\dfrac{13}{12}\)
\(x=\dfrac{13}{12}-\dfrac{7}{8}\)
\(x=\dfrac{104}{96}-\dfrac{84}{96}\)
\(x=\dfrac{5}{24}\)
\(b)\) \(\dfrac{-6}{12}-x=\dfrac{9}{48}\)
\(\dfrac{-1}{2}-x=\dfrac{3}{16}\)
\(x=\dfrac{-1}{2}-\dfrac{3}{16}\)
\(x=\dfrac{-8}{16}-\dfrac{3}{16}\)
\(x=\dfrac{-11}{16}\)
\(c)\) \(x+\dfrac{4}{6}=\dfrac{5}{25}-\left(-\dfrac{7}{15}\right)\)
\(x+\dfrac{4}{6}=\dfrac{5}{25}+\dfrac{7}{15}\)
\(x+\dfrac{4}{6}=\dfrac{75}{375}+\dfrac{105}{375}\)
\(x+\dfrac{4}{6}=\dfrac{12}{25}\)
\(x=\dfrac{12}{25}-\dfrac{4}{6}\)
\(x=\dfrac{72}{150}-\dfrac{100}{150}\)
\(x=\dfrac{-14}{75}\)
\(d)\) \(x+\dfrac{4}{5}=\dfrac{6}{20}-\left(-\dfrac{7}{3}\right)\)
\(x+\dfrac{4}{5}=\dfrac{6}{20}+\dfrac{7}{3}\)
\(x+\dfrac{4}{5}=\dfrac{18}{60}+\dfrac{140}{60}\)
\(x+\dfrac{4}{5}=\dfrac{79}{30}\)
\(x=\dfrac{79}{30}-\dfrac{4}{5}\)
\(x=\dfrac{79}{30}-\dfrac{24}{30}\)
\(x=\dfrac{11}{6}\)
\(\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{900}-1\right)\)
\(=\left(\frac{1}{2}-1\right)\left(\frac{1}{2}+1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{3}+1\right)\left(\frac{1}{4}-1\right)\left(\frac{1}{4}+1\right)...\left(\frac{1}{30}-1\right)\left(\frac{1}{30}+1\right)\)
\(=\frac{-1}{2}.\frac{3}{2}.\frac{-2}{3}.\frac{4}{3}.\frac{-3}{4}.\frac{5}{4}...\frac{-29}{30}.\frac{31}{30}=-\frac{31}{60}\)
(14−1)(19−1)(116−1)...(1900−1)(14−1)(19−1)(116−1)...(1900−1)
=(12−1)(12+1)(13−1)(13+1)(14−1)(14+1)...(130−1)(130+1)=(12−1)(12+1)(13−1)(13+1)(14−1)(14+1)...(130−1)(130+1)
=−12.32.−23.43.−34.54...−2930.3130=−3160