Biết x/3=5/3;y/z=2/7 và x+3y+2z=280.Tính C=3x-4y+z
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HN
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.\(\frac{x}{y}=\frac{4}{3}\Rightarrow\hept{\begin{cases}x=4a\\y=3a\\x-y=4a-3a=a\end{cases}}\\ \left(x-y\right)^{2015}=5^{2015}\Rightarrow x-y=5\\ \Rightarrow a=5\Rightarrow\hept{\begin{cases}x=4\times5=20\\y=3\times5=15\end{cases}}\)
L
0
6 tháng 3 2023
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
L
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 \(x\in\left\{3;-11;-4\right\}\)
DM
0
KS
0
PT
1
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
6 tháng 11 2018
Đặt \(C=3+3^3+3^5+..+3^{203}\)
\(\Rightarrow B=1+C\Rightarrow8B=8+8C\)
\(3^2.C=9.C=3^3+3^5+3^7+...+3^{205}\)
\(8.C=9.C-C=3^{205}-3\)
\(\Rightarrow8B=8+3^{205}-3=3^{205}+5\)
\(\Rightarrow8B-5=3^{5x}\Leftrightarrow3^{205}+5-5=3^{5x}\Leftrightarrow3^{205}=3^{5x}\Rightarrow205=5x\Rightarrow x=205:5=41\)
MP
1
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
C
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) \(\dfrac{x}{5}:\dfrac{3}{8}=\dfrac{8}{5}\)
\(\dfrac{x}{5}=\dfrac{8}{5}\times\dfrac{3}{8}\)
\(\dfrac{x}{5}=\dfrac{3}{5}\)
\(=>x=3\)