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KT
19 tháng 2 2018
\(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0\)
\(\Leftrightarrow\)\(\frac{x+2}{327}+1+\frac{x+3}{326}+1+\frac{x+4}{325}+1+\frac{x+5}{324}+1 +\frac{x+349}{5}-4=0\)
\(\Leftrightarrow\)\(\frac{x+329}{327}+\frac{x+329}{326}+\frac{x+329}{325}+\frac{x+329}{324}+\frac{x+329}{5}=0\)
\(\Leftrightarrow\)\(\left(x+329\right)\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)=0\)
\(\Leftrightarrow\)\(x+329=0\) (vì 1/327 + 1/326 + 1/325 + 1/324 + 1/5 khác 0 )
\(\Leftrightarrow\)\(x=-329\)
19 tháng 2 2018
Bài 1 :
\(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0\)
\(\Leftrightarrow\)\(\left(\frac{x+2}{327}+1\right)+\left(\frac{x+3}{326}+1\right)+\left(\frac{x+4}{325}+1\right)+\left(\frac{x+5}{324}+1\right)+\left(\frac{x+349}{5}-4\right)=0\)
\(\Leftrightarrow\)\(\frac{x+329}{327}+\frac{x+329}{326}+\frac{x+329}{325}+\frac{x+329}{324}+\frac{x+329}{5}=0\)
\(\Leftrightarrow\)\(\left(x+329\right)\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)=0\)
Vì \(\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)\ne0\)
\(\Rightarrow\)\(x+329=0\)
\(\Rightarrow\)\(x=-329\)
Vậy \(x=-329\)
PL
6 tháng 3 2020
1. A = 75(42004 + 42003 +...+ 42 + 4 + 1) + 25
A = 25 . [3 . (42004 + 42003 +...+ 42 + 4 + 1) + 1]
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 3 + 1)
A = 25 . (3 . 42004 + 3 . 42003 +...+ 3 . 42 + 3 . 4 + 4)
A = 25 . 4 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1)
A =100 . (3 . 42003 + 3 . 42002 +...+ 3 . 4 + 3 + 1) \(⋮\) 100
20 tháng 12 2018
a) \(\frac{1}{4}+\frac{1}{3}:2x=-5\)
\(\frac{1}{3}:2x=\frac{-21}{4}\)
\(2x=\frac{-4}{63}\)
\(x=\frac{2}{63}\)
20 tháng 12 2018
b) \(\left(3x-\frac{1}{4}\right)\left(x+\frac{1}{2}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x-\frac{1}{4}=0\\x+\frac{1}{2}=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{12}\\x=\frac{-1}{2}\end{cases}}\)
Vậy.........
28 tháng 11 2016
Bài 2:
a) \(\left|x+1\right|+\left|x+2\right|+\left|x+4\right|+\left|x+5\right|-6x=0\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+4\right|+\left|x+5\right|=6x\)
Ta có: \(\left|x+1\right|\ge0;\left|x+2\right|\ge0;\left|x+4\right|\ge0;\left|x+5\right|\ge0\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+4\right|+\left|x+5\right|\ge0\)
\(\Rightarrow6x\ge0\)
\(\Rightarrow x\ge0\)
\(\Rightarrow\left|x+1\right|+\left|x+2\right|+\left|x+4\right|+\left|x+5\right|=x+1+x+2+x+4+x+5=6x\)
\(\Rightarrow4x+12=6x\)
\(\Rightarrow2x=12\)
\(\Rightarrow x=6\)
Vậy x = 6
b) Giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x-2}{2}=\frac{y-3}{3}=\frac{z-3}{4}=\frac{2y-6}{6}=\frac{3z-9}{12}=\frac{x-2-2y+6+3z-9}{2-6+12}=\frac{\left(x-2y+3z\right)-\left(2-6+9\right)}{8}\)
\(=\frac{14-5}{8}=\frac{9}{8}\)
+) \(\frac{x-2}{2}=\frac{9}{8}\Rightarrow x-2=\frac{9}{4}\Rightarrow x=\frac{17}{4}\)
+) \(\frac{y-3}{3}=\frac{9}{8}\Rightarrow y-3=\frac{27}{8}\Rightarrow y=\frac{51}{8}\)
+) \(\frac{z-3}{4}=\frac{9}{8}\Rightarrow z-3=\frac{9}{2}\Rightarrow z=\frac{15}{2}\)
Vậy ...
c) \(5^x+5^{x+1}+5^{x+2}=3875\)
\(\Rightarrow5^x+5^x.5+5^x.5^2=3875\)
\(\Rightarrow5^x.\left(1+5+5^2\right)=3875\)
\(\Rightarrow5^x.31=3875\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
Vậy x = 3
HH
29 tháng 2 2020
\(\frac{1}{3}-|\frac{5}{4}-2x|=\frac{1}{4}\)
\(\Leftrightarrow|\frac{5}{4}-2x|=\frac{1}{4}+\frac{1}{3}=\frac{7}{12}\)
\(\Leftrightarrow\orbr{\begin{cases}Th1:\frac{5}{4}-2x=\frac{7}{12}\\Th2:\frac{5}{4}-2x=-\frac{7}{12}\end{cases}}\)
\(\Leftrightarrow Th1:\frac{5}{4}-2x=\frac{7}{12}\) \(\Leftrightarrow Th2:\frac{5}{4}-2x=-\frac{7}{12}\)
\(\Leftrightarrow2x=\frac{7}{12}+\frac{5}{4}\) \(\Leftrightarrow2x=-\frac{7}{12}+\frac{5}{4}\)
\(\Leftrightarrow2x=\frac{11}{6}\) \(\Leftrightarrow2x=\frac{2}{3}\)
\(\Leftrightarrow x=\frac{11}{12}\) \(\Leftrightarrow x=\frac{1}{3}\)
P/s : Mình làm bừa ạ nếu kh đúng xin mọi người chỉ thêm ~~
VM
25 tháng 11 2019
1.
a) \(x-4\sqrt{x}=0\)
\(\Rightarrow\sqrt{x}.\left(\sqrt{x}-4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\\sqrt{x}=0+4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\\sqrt{x}=4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=16\end{matrix}\right.\)
Vậy \(x\in\left\{0;16\right\}.\)
b) \(\left|\frac{3}{5}\sqrt{x}-\frac{1}{20}\right|-\frac{3}{4}=\frac{1}{5}\)
\(\Rightarrow\left|\frac{3}{5}\sqrt{x}-\frac{1}{20}\right|=\frac{1}{5}+\frac{3}{4}\)
\(\Rightarrow\left|\frac{3}{5}\sqrt{x}-\frac{1}{20}\right|=\frac{19}{20}.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{3}{5}\sqrt{x}-\frac{1}{20}=\frac{19}{20}\\\frac{3}{5}\sqrt{x}-\frac{1}{20}=-\frac{19}{20}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\frac{3}{5}\sqrt{x}=1\\\frac{3}{5}\sqrt{x}=-\frac{9}{10}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}\sqrt{x}=1:\frac{3}{5}\\\sqrt{x}=\left(-\frac{9}{10}\right):\frac{3}{5}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x}=\frac{5}{3}\\\sqrt{x}=-\frac{3}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{25}{9}\\x\in\varnothing\end{matrix}\right.\)
Vậy \(x=\frac{25}{9}.\)
Câu c) làm tương tự như câu b).
Chúc bạn học tốt!
MT
Tìm x, biét
1 . \(\sqrt{2x+\frac{5}{4}}=\frac{3}{2}\)
2 \(\sqrt{\frac{x}{3}-\frac{7}{6}}=\frac{1}{6}\)
1
5 tháng 11 2015
a) \(\sqrt{2x+\frac{5}{4}}=\frac{3}{2}\)
\(2x+\frac{5}{4}=\frac{9}{4}\)
2x = 1
\(x=\frac{1}{2}\)
b) \(\sqrt{\frac{x}{3}-\frac{7}{6}}=\frac{1}{6}\)
\(\frac{x}{3}-\frac{7}{6}=\frac{1}{36}\)
\(\frac{x}{3}=\frac{43}{36}\)
\(x=\frac{43\cdot3}{36}=\frac{129}{36}\)
5 tháng 3 2022
a: \(\Leftrightarrow x\cdot\dfrac{4}{3}=\dfrac{5}{6}+\dfrac{1}{4}=\dfrac{13}{12}\)
\(\Leftrightarrow x=\dfrac{13}{12}:\dfrac{4}{3}=\dfrac{13}{12}\cdot\dfrac{3}{4}=\dfrac{39}{48}=\dfrac{13}{16}\)
b: \(\Leftrightarrow\left|x-\dfrac{1}{2}\right|=\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{5}{6}\)
=>x-1/2=5/6 hoặc x-1/2=-5/6
=>x=4/3 hoặc x=-1/3
c: \(\left(x+20\right)^{100}+\left|y+4\right|=0\)
=>x+20=0 và y+4=0
=>x=-20 và y=-4