1/x(x+3) + 1/(x+3)(x+6) +1/(x+6)(x+9) + 1/(x+9)(x+12) =1/16
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DT
1
20 tháng 3 2023
\(\Leftrightarrow\dfrac{3}{x\left(x+3\right)}+\dfrac{3}{\left(x+3\right)\left(x+6\right)}+...+\dfrac{3}{\left(x+9\right)\left(x+12\right)}=\dfrac{3}{16}\)
=>\(\dfrac{1}{x}-\dfrac{1}{x+3}+\dfrac{1}{x+3}-\dfrac{1}{x+6}+...+\dfrac{1}{x+9}-\dfrac{1}{x+12}=\dfrac{3}{16}\)=>\(\dfrac{1}{x}-\dfrac{1}{x+12}=\dfrac{3}{16}\)
=>\(\dfrac{x+12-x}{x\left(x+12\right)}=\dfrac{3}{16}\)
=>12/x(x+12)=3/16
=>4/x(x+12)=1/16
=>x(x+12)=64
=>x^2+12x-64=0
=>x^2+16x-4x-64=0
=>(x+16)(x-4)=0
=>x=4 hoặc x=-16
DT
2
C
11 tháng 1 2017
Ta có :1.2+2.4+3.6+4.8+5.10/3.4+6.8+9.12+12.16+15.20=[1.2(1+4+9+...+25)]/[3.4(1+4+9+16)]
=(1.2)/(3.4)=2/12=1/6
CHÚC BẠN HỌC TỐT!!
cho tớ nhé!!!!
20 tháng 6 2015
Tính nhanh mỗi biểu thức sau:
a, 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20
= (0 + 20) + (1 + 19) + (2 + 18) + (3 + 17) + (4 + 16) + (5 + 15) + (6 + 14) + (7 + 13) + (8 + 12) + (9 + 11) + 10
= 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 10
= 20 x 10 + 10
= 200 + 10
= 210
b, 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x (4 x 9 - 36)
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x (36 - 36)
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 0
= A x 0
= 0
c, (81 - 7 x 9 - 18) : (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= (81 - 63 - 18) : (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= (18 - 18) : (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= 0 :(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= 0 : A
= 0
d, (6 x 5 + 7 - 37) x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (30 + 7 - 37) x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (37 - 37) x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= 0 x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= 0 x A
= 0
e, (11 x 9 - 100 + 1) : (1 x 2 x 3 x 4 x ... x 10)
= (99 - 100 + 1) : (1 x 2 x 3 x 4 x ... x 10)
= (99 + 1 - 100) : (1 x 2 x 3 x 4 x ... x 10)
= (100 - 100) : (1 x 2 x 3 x 4 x ... x 10)
= 0 : (1 x 2 x 3 x 4 x ... x 10)
= 0 : A
= 0
g, (m : 1 - m x 1) : (m x 2008 + m x 2008)
= (m - m) : (m x 2008 + m x 2008)
= 0 : (m x 2008 + m x 2008)
= 0 : A
= 0
h, (2 + 4 + 6 + 8 + m x n) x (324 x 3 - 972)
= (2 + 4 + 6 + 8 + m x n) x (972 - 972)
= (2 + 4 + 6 + 8 + m x n) x 0
= A x 0
= 0
l, (1 + 2 + 3 + ... + 99) x (13 x 15 - 12 x 15 - 15)
= (1 + 2 + 3 + ... + 99) x (15 x (13 - 12 - 1))
= (1 + 2 + 3 + ... + 99) x (15 x 0)
= (1 + 2 + 3 + ... + 99) x 0
= A x 0
= 0
i, (0 x 1 x 2 x...x 99 x 100) : (2 + 4 + 6 +...+ 98)
= 0 x : (2 + 4 + 6 +...+ 98)
= 0 x A
= 0
k, (0 + 1 + 2 +...+ 97 + 99) x (45 x 3 - 45 x 2 - 45)
= (0 + 1 + 2 +...+ 97 + 99) x (45 x (3 - 2 - 4))
= (0 + 1 + 2 +...+ 97 + 99) x (45 x 0)
= (0 + 1 + 2 +...+ 97 + 99) x 0
= A x 0
= 0
LM
Lê Minh Vũ
CTVHS
VIP
7 tháng 7 2023
\(4,7\div0,25+5,3\times4\)
\(=18,8+21,2\)
\(=40\)
\(3\times\left(a-2\right)+150=240\)
\(3\times\left(a-2\right)=90\)
\(a-2=30\)
\(a=32\)
\(\dfrac{1}{9}+a+\dfrac{7}{12}=\dfrac{17}{18}\)
\(\dfrac{1}{9}+a=\dfrac{13}{36}\)
\(a=\dfrac{1}{4}\)
\(\left(\dfrac{1}{2}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}+\dfrac{1}{4}\times\dfrac{1}{5}+\dfrac{1}{5}\times\dfrac{1}{6}+\dfrac{1}{6}\times\dfrac{1}{7}+\dfrac{1}{7}\times\dfrac{1}{8}\right)\times a=\dfrac{9}{16}\)
\(\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}\right)\times a=\dfrac{9}{16}\)
\(\left(\dfrac{1}{2}-\dfrac{1}{8}\right)\times a=\dfrac{9}{16}\)
\(\dfrac{3}{8}\times a=\dfrac{9}{16}\)
\(a=\dfrac{3}{2}\)
3 tháng 7 2021
Giải:
a) \(\dfrac{-5}{8}=\dfrac{x}{16}\)
\(\Rightarrow x=\dfrac{16.-5}{8}=-10\)
\(\dfrac{3x}{9}=\dfrac{2}{6}\)
\(\Rightarrow3x=\dfrac{2.9}{6}=3\)
\(\Rightarrow x=1\)
b) \(\dfrac{x+3}{15}=\dfrac{1}{3}\)
\(\Rightarrow x+3=\dfrac{1.15}{3}=5\)
\(\Rightarrow x=2\)
\(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
\(\Rightarrow2x+1=\dfrac{6.7}{2}=21\)
\(\Rightarrow x=10\)
c) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\Rightarrow\dfrac{4}{x-6}=\dfrac{-12}{18}\)
\(\Rightarrow x-6=\dfrac{18.4}{-12}=-6\)
\(\Rightarrow x=0\)
\(\Rightarrow\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\Rightarrow y=\dfrac{-12.24}{18}=-16\)
\(\dfrac{3-x}{-12}=\dfrac{16}{y+1}=\dfrac{192}{-72}\)
\(\Rightarrow\dfrac{3-x}{-12}=\dfrac{192}{-72}\)
\(\Rightarrow3-x=\dfrac{192.-12}{-72}=32\)
\(\Rightarrow x=-29\)
\(\Rightarrow\dfrac{16}{y+1}=\dfrac{192}{-72}\)
\(\Rightarrow y+1=\dfrac{16.-72}{192}=-6\)
d) \(\dfrac{-2}{3}< \dfrac{x}{5}< \dfrac{-1}{6}\)
\(\Rightarrow\dfrac{-20}{30}< \dfrac{6x}{30}< \dfrac{-5}{30}\)
\(\Rightarrow6x\in\left\{-18;-12;-6\right\}\)
\(\Rightarrow x\in\left\{-3;-2;-1\right\}\)
\(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\)
\(\Rightarrow\dfrac{-8}{40}\le\dfrac{5x}{40}\le\dfrac{10}{40}\)
\(\Rightarrow5x\in\left\{-5;0;5;10\right\}\)
\(\Rightarrow x\in\left\{-1;0;1;2\right\}\)
e) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\)
\(\Rightarrow\dfrac{x+46}{20}=x+\dfrac{2}{5}\)
\(\Rightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\)
\(\Rightarrow5.\left(x+46\right)=20.\left(5x+2\right)\)
\(\Rightarrow5x+230=100x+40\)
\(\Rightarrow5x-100x=40-230\)
\(\Rightarrow-95x=-190\)
\(\Rightarrow x=-190:-95\)
\(\Rightarrow x=2\)
\(y\dfrac{5}{y}=\dfrac{86}{y}\)
\(\Rightarrow y+\dfrac{5}{y}=\dfrac{86}{y}\)
\(\Rightarrow\dfrac{y^2+5}{y}=\dfrac{86}{y}\)
\(\Rightarrow y^2+5=86\)
\(\Rightarrow y^2=86-5\)
\(\Rightarrow y^2=81\)
\(\Rightarrow\left[{}\begin{matrix}y=9\\y=-9\end{matrix}\right.\)
Chúc bạn học tốt!
4 tháng 2 2020
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