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14 tháng 8
a: ||\(x:\left(-\frac23\right)+\frac12\) |+\(\frac56\) |\(\cdot\frac12=\frac34\)
=>||\(x:\left(-\frac23\right)+\frac12\) |\(+\frac56\) |\(=\frac34:\frac12=\frac32\)
mà \(\left|x:\left(-\frac23\right)+\frac12\right|+\frac56\ge\frac56\)
nên \(\left|x:\left(-\frac23\right)+\frac12\right|+\frac56=\frac32\)
=>\(\left|x:\left(-\frac23\right)+\frac12\right|=\frac32-\frac56=\frac96-\frac56=\frac46=\frac23\)
=>\(\left[\begin{array}{l}x:\left(-\frac23\right)+\frac12=\frac23\\ x:\left(-\frac23\right)+\frac12=-\frac23\end{array}\right.\Rightarrow\left[\begin{array}{l}x:\left(-\frac23\right)=\frac23-\frac12=\frac16\\ x:\left(-\frac23\right)=-\frac23-\frac12=-\frac46-\frac36=-\frac76\end{array}\right.\)
=>\(\left[\begin{array}{l}x=\frac16\cdot\left(-\frac23\right)=-\frac{2}{18}=-\frac19\\ x=-\frac76\cdot\left(-\frac23\right)=\frac{14}{18}=\frac79\end{array}\right.\)
a: \(\left|-\frac23x+\frac38\right|\cdot\left(-\frac85\right)=-\frac{8}{15}\)
=>\(\left|\frac23x-\frac38\right|=\frac{8}{15}:\frac85=\frac{5}{15}=\frac13\)
=>\(\left[\begin{array}{l}\frac23x-\frac38=\frac13\\ \frac23x-\frac38=-\frac13\end{array}\right.\Rightarrow\left[\begin{array}{l}\frac23x=\frac38+\frac13=\frac{17}{24}\\ \frac23x=-\frac13+\frac38=\frac{1}{24}\end{array}\right.\)
=>\(\left[\begin{array}{l}x=\frac{17}{24}:\frac23=\frac{17}{24}\cdot\frac32=\frac{17}{16}\\ x=\frac{1}{24}:\frac23=\frac{1}{24}\cdot\frac32=\frac{3}{48}=\frac{1}{16}\end{array}\right.\)
24 tháng 9
a: \(\frac{x-100}{24}+\frac{x-98}{26}+\frac{x-96}{28}=3\)
=>\(\left(\frac{x-100}{24}-1\right)+\left(\frac{x-98}{26}-1\right)+\left(\frac{x-96}{28}-1\right)=0\)
=>\(\frac{x-124}{24}+\frac{x-124}{26}+\frac{x-124}{28}=0\)
=>\(\left(x-124\right)\left(\frac{1}{24}+\frac{1}{26}+\frac{1}{28}\right)=0\)
=>x-124=0
=>x=124
b: \(\frac{x-1}{65}+\frac{x-3}{63}=\frac{x-5}{61}+\frac{x-7}{59}\)
=>\(\left(\frac{x-1}{65}-1\right)+\left(\frac{x-3}{63}-1\right)=\left(\frac{x-5}{61}-1\right)+\left(\frac{x-7}{59}-1\right)\)
=>\(\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
=>\(\left(x-66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
=>x-66=0
=>x=66
c: \(\frac{x-28-124}{2011}+\frac{x-124-2011}{28}+\frac{x-2011-28}{124}=3\)
=>\(\left(\frac{x-28-124}{2011}-1\right)+\left(\frac{x-124-2011}{28}-1\right)+\left(\frac{x-28-2011}{124}-1\right)=0\)
=>x-28-124-2011=0
=>x=2011+124+28
=>x=2163
19 tháng 9
d: \(\frac27-\left(\frac23+2x\right)=\frac57\)
=>\(2x+\frac23=\frac27-\frac57=-\frac37\)
=>\(2x=-\frac37-\frac23=-\frac{9}{21}-\frac{14}{21}=-\frac{23}{21}\)
=>\(x=-\frac{23}{21}:2=-\frac{23}{42}\)
e: \(\frac12-2x=\left(-\frac12\right)^3\)
=>\(\frac12-2x=-\frac18\)
=>\(2x=\frac12+\frac18=\frac58\)
=>\(x=\frac58:2=\frac{5}{16}\)
f: \(\left(2x-3\right)\left(\frac34x+1\right)=0\)
=>\(\left[\begin{array}{l}2x-3=0\\ \frac34x+1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=3\\ \frac34x=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac32\\ x=-\frac43\end{array}\right.\)
g: \(\frac{7}{12}-\left(x+\frac76\right):\frac65=-\frac54\)
=>\(\left(x+\frac76\right):\frac65=\frac{7}{12}+\frac54=\frac{7}{12}+\frac{15}{12}=\frac{22}{12}=\frac{11}{6}\)
=>\(x+\frac76=\frac{11}{6}\cdot\frac65=\frac{11}{5}\)
=>\(x=\frac{11}{5}-\frac76=\frac{66}{30}-\frac{35}{30}=\frac{31}{30}\)
h: \(\frac34:\left(x+\frac12\right)-\frac56=-\frac14\)
=>\(\frac34:\left(x+\frac12\right)=-\frac14+\frac56=-\frac{3}{12}+\frac{10}{12}=\frac{7}{12}\)
=>\(x+\frac12=\frac34:\frac{7}{12}=\frac34\cdot\frac{12}{7}=\frac{36}{28}=\frac97\)
=>\(x=\frac97-\frac12=\frac{18}{14}-\frac{7}{14}=\frac{11}{14}\)
i: \(\frac25x+\frac35x=\frac34\)
=>\(x\left(\frac25+\frac35\right)=\frac34\)
=>\(x\cdot\frac55=\frac34\)
=>\(x=\frac34\)
k: \(\frac12x+\frac23x-x=\frac13\)
=>\(x\left(\frac12+\frac23-1\right)=\frac13\)
=>\(x\left(\frac12-\frac13\right)=\frac13\)
=>\(x\cdot\frac16=\frac13\)
=>\(x=\frac13:\frac16=2\)
l: \(\left(\frac32-\frac{2}{-5}\right):x-\frac12=\frac32\)
=>\(\left(\frac32+\frac25\right):x=\frac32+\frac12=2\)
=>\(\left(\frac{15}{10}+\frac{4}{10}\right):x=2\)
=>\(\frac{19}{10}:x=2\)
=>\(x=\frac{19}{10}:2=\frac{19}{20}\)
m: \(\left(5x-1\right)\left(2x-\frac13\right)=0\)
=>\(\left[\begin{array}{l}5x-1=0\\ 2x-\frac13=0\end{array}\right.\Rightarrow\left[\begin{array}{l}5x=1\\ 2x=\frac13\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac15\\ x=\frac16\end{array}\right.\)
Có 9999..99(gồm n chữ số 9)=[10^n-1].
Áp dụng:
11.11(2n chs 1)=\(\frac{10^{2n}-1}{9}\) , 111...1(n+1 chữ số 1)=\(\frac{10^{n+1}-1}{9}\),666....6(n chữ số 6)=\(\frac{10^{n}-1}{9}\) .6.
=> 11...1(2n chữ số 1)+111...1(n+1 chữ số 1)+666...66(n chữ số 1)+8=.....=\(\left(\frac{10^{n}+8}{3}\right)^2\) là 1 scp.