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19 tháng 5 2021

1.
\(\left(\frac{3}{1\times3}+\frac{3}{3\times5}+\frac{3}{5\times7}+...+\frac{3}{97\times99}\right)-x:\frac{3}{2}=\frac{7}{3}\\ \left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{97\times99}\right):\frac{3}{2}-x:\frac{3}{2}=\frac{7}{3}\\\left[\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)-x\right]:\frac{3}{2}=\frac{7}{3}\\ \left(1-\frac{1}{99}\right)-x=\frac{7}{3}\times\frac{3}{2}\\ \frac{98}{99}-x=\frac{7}{2}\\ x=\frac{98}{99}-\frac{7}{2}=\frac{-497}{198}\)

2.\(\frac{x}{y}=\frac{4}{3}\Rightarrow\hept{\begin{cases}x=4a\\y=3a\\x-y=4a-3a=a\end{cases}}\\ \left(x-y\right)^{2015}=5^{2015}\Rightarrow x-y=5\\ \Rightarrow a=5\Rightarrow\hept{\begin{cases}x=4\times5=20\\y=3\times5=15\end{cases}}\)

22 tháng 12 2021

1.
(31×3+33×5+35×7+...+397×99)−x:32=73(21×3+23×5+25×7+...+297×99):32−x:32=73[(1−13+13−15+15−17+...+197−199)−x]:32=73(1−199)−x=73×32

a: =>x=3/7+3/5=15/35+21/35=36/35

b: =>x/35=4/5-5/7=28/35-25/35=3/35

=>x=3

c: =>x<3/4+8/4=11/4

=>\(x\in\left\{0;1;2;3\right\}\)

d: =>5/3<x<5/6+24/6=29/6

=>\(x\in\left\{2;3;4\right\}\)

e: =>x<10/12-9/12=1/12

=>x=0

f: =>2/3<x<12/6-5/6=7/6

=>x=1

26 tháng 10 2022

\(\Leftrightarrow\left[3x+3-2x-6\right]^3+\left[2x+6-x+5\right]^3+\left[x-5-3x-3\right]^3=0\)

=>(x-3)^3+(x+11)^3+(-2x-8)^3=0

Đặt x-3=a; x+11=b

=>a^3+b^3-(a+b)^3=0

=>3ab(a+b)=0

=>(x-3)(x+11)(2x+8)=0

hay \(x\in\left\{3;-11;-4\right\}\)

6 tháng 11 2018

Đặt  \(C=3+3^3+3^5+..+3^{203}\)

\(\Rightarrow B=1+C\Rightarrow8B=8+8C\)

\(3^2.C=9.C=3^3+3^5+3^7+...+3^{205}\)

\(8.C=9.C-C=3^{205}-3\)

\(\Rightarrow8B=8+3^{205}-3=3^{205}+5\)

\(\Rightarrow8B-5=3^{5x}\Leftrightarrow3^{205}+5-5=3^{5x}\Leftrightarrow3^{205}=3^{5x}\Rightarrow205=5x\Rightarrow x=205:5=41\)

29 tháng 4 2019

Ta có: \(\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{x.\left(x+2\right)}=\frac{8}{7}\)

\(\Leftrightarrow3\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{x.\left(x+2\right)}\right)=\frac{8}{7}\)

\(\Leftrightarrow3.\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{x\left(x+2\right)}\right).\frac{1}{2}=\frac{8}{7}\)

\(\Leftrightarrow\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{8}{7}\)

\(\Leftrightarrow\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{x+2}\right)=\frac{8}{7}\)

\(\Leftrightarrow\frac{1}{3}-\frac{1}{x+2}=\frac{8}{7}:\frac{3}{2}=\frac{8}{7}.\frac{2}{3}=\frac{16}{21}\)

\(\Leftrightarrow\frac{1}{x+2}=\frac{1}{3}-\frac{16}{21}=\frac{-3}{7}\)

\(\Leftrightarrow\frac{-3}{-3\left(x+2\right)}=\frac{-3}{7}\)

\(\Leftrightarrow-3\left(x+2\right)=7\)

\(\Leftrightarrow x+2=\frac{7}{-3}\)

\(\Leftrightarrow x=\frac{7}{-3}-2=\frac{-13}{3}\)

Vậy \(x=\frac{-13}{3}\)

18 tháng 10 2015

x^5=x      

=>x=0 hặc 1      

(2x+1)^3=125. 

(2x+1)3=53

=>2x+1=5

2x=5-1

2x=4

x=4:2

x=2

18 tháng 10 2015

A =3+32+33+...+3100

3A=3(3+32+33+...+3100)

3A=32+33+34+...+3101

3A-A=(32+33+34+...+3101)-(3+32+33+...+3100)

2A=3101-3

=>2A+3=3^n

3101-3+3=3n

3101=3n

vậy n=101

22 tháng 5 2022

a) \(\dfrac{3}{5}:x=3\)

\(x=\dfrac{3}{5}:3\)

\(x=\dfrac{3}{5}\times\dfrac{1}{3}\)

\(x=\dfrac{1}{5}\)

b) \(\dfrac{x}{5}:\dfrac{3}{8}=\dfrac{8}{5}\)

\(\dfrac{x}{5}=\dfrac{8}{5}\times\dfrac{3}{8}\)

\(\dfrac{x}{5}=\dfrac{3}{5}\)

\(=>x=3\)

22 tháng 5 2022

a,x=3/5:3/

x=3/5.1/3

x=1/5

b,x/5=8/5.3/8

x/5=3/5

=> x=3